UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                  SCHEDULE 13G

                   UNDER THE SECURITIES EXCHANGE ACT OF 1934
                               (AMENDMENT NO. 2)*

                         Alexion Pharmaceuticals, Inc.
--------------------------------------------------------------------------------
                                (Name of Issuer)

                    Common Stock, $.0001 Par Value Per Share
--------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    01531109
                                    --------
                                 (CUSIP Number)

                               December 31, 2005
                               -----------------
                      (Date of Event which Requires Filing
                               of this Statement)



Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

                  [ ]      Rule 13d-1(b)
                  [X]      Rule 13d-1(c)
                  [ ]      Rule 13d-1(d)



  *The remainder of this cover page shall be filled out for a reporting person's
  initial filing on this form with respect to the subject class of securities,
  and for any subsequent amendment containing information which would alter the
  disclosures provided in a prior cover page.

  The information required on the remainder of this cover page shall not be
  deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
  Act of 1934 ("Act") or otherwise subject to the liabilities of that section of
  the Act but shall be subject to all other provisions of the Act (however, see
  the Notes).



                                  Page 1 of 10



--------------------------                                  -------------------
CUSIP No. 01531109                    13G                   Page 2 of 10 Pages
--------------------------                                  -------------------

---------- --------------------------------------------------------------------
        1  NAME OF REPORTING PERSON
           I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

           S.A.C. Capital Advisors, LLC
---------- --------------------------------------------------------------------
        2  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                 (a)    |_|

                                                 (b)    |X|

---------- --------------------------------------------------------------------
        3  SEC USE ONLY
---------- --------------------------------------------------------------------
        4  CITIZENSHIP OR PLACE OF ORGANIZATION

           Delaware
--------------------- ----- ---------------------------------------------------
                         5  SOLE VOTING POWER

                            0
      NUMBER OF       ----- ---------------------------------------------------
        SHARES           6  SHARED VOTING POWER
     BENEFICIALLY
        OWNED               3,000 (see Item 4)
          BY          ----- ---------------------------------------------------
         EACH            7  SOLE DISPOSITIVE POWER
      REPORTING
        PERSON              0
         WITH         ----- ---------------------------------------------------
                         8  SHARED DISPOSITIVE POWER

                            3,000 (see Item 4)
---------- --------------------------------------------------------------------
        9  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           3,000 (see Item 4)
---------- --------------------------------------------------------------------
       10  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

           |_|
---------- --------------------------------------------------------------------
       11  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

           Less than 0.1% (see Item 4)
---------- --------------------------------------------------------------------
       12  TYPE OF REPORTING PERSON*

           00
---------- --------------------------------------------------------------------
                       *SEE INSTRUCTION BEFORE FILLING OUT


                                  Page 2 of 10



--------------------------                                  -------------------
CUSIP No. 01531109                    13G                   Page 3 of 10 Pages
--------------------------                                  -------------------

---------- --------------------------------------------------------------------
        1  NAME OF REPORTING PERSON
           I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

           S.A.C. Capital Management, LLC
---------- --------------------------------------------------------------------
        2  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                      (a)      |_|

                                                      (b)      |X|

---------- --------------------------------------------------------------------
        3  SEC USE ONLY
---------- --------------------------------------------------------------------
        4  CITIZENSHIP OR PLACE OF ORGANIZATION

           Delaware
-------------------- ------ ---------------------------------------------------
                         5  SOLE VOTING POWER

                            0
      NUMBER OF      ------ ---------------------------------------------------
       SHARES            6  SHARED VOTING POWER
    BENEFICIALLY
        OWNED               3,000 (see Item 4)
         BY          ------ ---------------------------------------------------
        EACH             7  SOLE DISPOSITIVE POWER
      REPORTING
       PERSON               0
        WITH         ------ ---------------------------------------------------
                         8  SHARED DISPOSITIVE POWER

                            3,000 (see Item 4)
---------- --------------------------------------------------------------------
        9  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           3,000 (see Item 4)
---------- --------------------------------------------------------------------
       10  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

           |_|
---------- --------------------------------------------------------------------
       11  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

           Less than 0.1% (see Item 4)
---------- --------------------------------------------------------------------
       12  TYPE OF REPORTING PERSON*

           00
---------- --------------------------------------------------------------------
                       *SEE INSTRUCTION BEFORE FILLING OUT


                                  Page 3 of 10



--------------------------                                  -------------------
CUSIP No. 01531109                    13G                   Page 4 of 10 Pages
--------------------------                                  -------------------

---------- --------------------------------------------------------------------
        1  NAME OF REPORTING PERSON
           I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

           Sigma Capital Management, LLC
---------- --------------------------------------------------------------------
        2  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                      (a)     |_|

                                                      (b)     |X|

---------- --------------------------------------------------------------------
        3  SEC USE ONLY
---------- --------------------------------------------------------------------
        4  CITIZENSHIP OR PLACE OF ORGANIZATION

           Delaware
-------------------- ------ ---------------------------------------------------
                         5  SOLE VOTING POWER

                            0
      NUMBER OF      ------ ---------------------------------------------------
       SHARES            6  SHARED VOTING POWER
    BENEFICIALLY
        OWNED               0 (see Item 4)
         BY          ------ ---------------------------------------------------
        EACH             7  SOLE DISPOSITIVE POWER
      REPORTING
       PERSON               0
        WITH         ------ ---------------------------------------------------
                         8  SHARED DISPOSITIVE POWER

                            0 (see Item 4)
---------- --------------------------------------------------------------------
        9  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           0 (see Item 4)
---------- --------------------------------------------------------------------
       10  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

           |_|
---------- --------------------------------------------------------------------
       11  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

           0% (see Item 4)
---------- --------------------------------------------------------------------
       12  TYPE OF REPORTING PERSON*

           00
---------- --------------------------------------------------------------------
                       *SEE INSTRUCTION BEFORE FILLING OUT

                                  Page 4 of 10



--------------------------                                  -------------------
CUSIP No. 01531109                    13G                   Page 5 of 10 Pages
--------------------------                                  -------------------

---------- --------------------------------------------------------------------
        1  NAME OF REPORTING PERSON
           I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

           Steven A. Cohen
---------- --------------------------------------------------------------------
        2  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                      (a)     |_|

                                                      (b)     |X|

---------- --------------------------------------------------------------------
        3  SEC USE ONLY
---------- --------------------------------------------------------------------
        4  CITIZENSHIP OR PLACE OF ORGANIZATION

           United States
-------------------- ------ ---------------------------------------------------
                         5  SOLE VOTING POWER

                            0
      NUMBER OF      ------ ---------------------------------------------------
       SHARES            6  SHARED VOTING POWER
    BENEFICIALLY
        OWNED               3,000 (see Item 4)
         BY          ------ ---------------------------------------------------
        EACH             7  SOLE DISPOSITIVE POWER
      REPORTING
       PERSON               0
        WITH         ------ ---------------------------------------------------
                         8  SHARED DISPOSITIVE POWER

                            3,000 (see Item 4)

---------- --------------------------------------------------------------------
        9  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           3,000 (see Item 4)
---------- --------------------------------------------------------------------
       10  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

           |_|
---------- --------------------------------------------------------------------
       11  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

           Less than 0.1% (see Item 4)
---------- --------------------------------------------------------------------
       12  TYPE OF REPORTING PERSON*

           IN
---------- --------------------------------------------------------------------
                       *SEE INSTRUCTION BEFORE FILLING OUT


                                  Page 5 of 10


ITEM 1(A)                      NAME OF ISSUER:
                               --------------

                               Alexion Pharmaceuticals, Inc.

ITEM 1(B)                      ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:
                               -----------------------------------------------

                               352 Knotter Drive
                               Cheshire, Connecticut 06410

ITEMS 2(A)                     NAME OF PERSON FILING:
                               ----------------------

                               This statement is filed by: (i) S.A.C.
                               Capital Advisors, LLC, ("SAC Capital
                               Advisors") with respect to shares of common
                               stock, $.0001 par value per share ("Shares")
                               of the Issuer beneficially owned by S.A.C.
                               MultiQuant Fund, LLC ("SAC MultiQuant") and
                               S.A.C. Arbitrage Fund, LLC ("SAC Arbitrage
                               Fund"); (ii) S.A.C. Capital Management, LLC,
                               ("SAC Capital Management") with respect to
                               Shares beneficially owned by SAC MultiQuant;
                               (iii) Sigma Capital Management, LLC ("Sigma
                               Capital Management"); and (iv) Steven A.
                               Cohen with respect to Shares beneficially
                               owned by SAC Capital Advisors, SAC Capital
                               Management and SAC MultiQuant.

ITEM 2(B)                      ADDRESS OF PRINCIPAL BUSINESS OFFICE:
                               -------------------------------------

                               The address of the principal business office
                               of (i) SAC Capital Advisors and Mr. Cohen is
                               72 Cummings Point Road, Stamford,
                               Connecticut 06902 and (ii) SAC Capital
                               Management and Sigma Capital Management is
                               540 Madison Avenue, New York, New York
                               10022.

ITEM 2(C)                      CITIZENSHIP:
                               ------------

                               SAC Capital Advisors, SAC Capital Management
                               and Sigma Capital Management are Delaware
                               limited liability companies. Mr. Cohen is a
                               United States citizen.

ITEM 2(D)                      TITLE OF CLASS OF SECURITIES:
                               -----------------------------

                               Common Stock, par value $.0001 per share


                                  Page 6 of 10


ITEM 2(E)       CUSIP NUMBER:
                -------------

                01531109

ITEM 3          Not Applicable

ITEM 4          OWNERSHIP:
                ----------

                The percentages used herein are calculated
                based upon the Shares issued and outstanding
                as of November 30, 2005 as reported on the
                Issuer's quarterly report on Form 10-Q filed
                with the Securities and Exchange Commission
                by the Company for the quarterly period
                ended October 31, 2005.

                1. S.A.C. Capital Advisors, LLC
                (a) Amount beneficially owned: 3,000
                (b) Percent of class: Less than 0.1%
                (c)(i) Sole power to vote or direct the vote: -0-
                (ii) Shared power to vote or direct the vote: 3,000
                (iii) Sole power to dispose or direct the disposition: -0-
                (iv) Shared power to dispose or direct the disposition: 3,000

                2. S.A.C. Capital Management, LLC
                (a) Amount beneficially owned: 3,000
                (b) Percent of class: Less than 0.1%
                (c)(i) Sole power to vote or direct the vote: -0-
                (ii) Shared power to vote or direct the vote: 3,000
                (iii) Sole power to dispose or direct the disposition: -0-
                (iv) Shared power to dispose or direct the disposition: 3,000

                3. Sigma Capital Management, LLC
                (a) Amount beneficially owned: -0-
                (b) Percent of class: 0%
                (c)(i) Sole power to vote or direct the vote: -0-
                (ii) Shared power to vote or direct the vote: -0-
                (iii) Sole power to dispose or direct the disposition: -0-
                (iv) Shared power to dispose or direct the disposition: -0-

                4. Steven A. Cohen
                (a) Amount beneficially owned: 3,000
                (b) Percent of class: Less than 0.1%
                (c)(i) Sole power to vote or direct the vote: -0-

                                  Page 7 of 10

                (ii) Shared power to vote or direct the vote: 3,000
                (iii) Sole power to dispose or direct the disposition: -0-
                (iv) Shared power to dispose or direct the disposition: 3,000

                SAC Capital Advisors, SAC Capital Management, Sigma Capital
                Management, and Mr. Cohen own directly no Shares. Pursuant to
                investment agreements, each of SAC Capital Advisors and SAC
                Capital Management share all investment and voting power with
                respect to the securities held by SAC MultiQuant. Pursuant to
                an investment management agreement, Sigma Capital Management
                maintains investment and voting power with respect to the
                securities held by Sigma Capital Associates. Mr. Cohen
                controls each of SAC Capital Advisors, SAC Capital Management
                and Sigma Capital Management. By reason of the provisions of
                Rule 13d-3 of the Securities Exchange Act of 1934, as amended,
                each of (i) SAC Capital Advisors, SAC Capital Management and
                Mr. Cohen may be deemed to own beneficially 3,000 Shares
                (constituting Less than 0.1% of the Shares outstanding). Each
                of SAC Capital Advisors, SAC Capital Management and Mr. Cohen
                disclaim beneficial ownership of any of the securities covered
                by this statement.

ITEM 5          OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS:
                --------------------------------------------

                If this statement is being filed to report the fact that as of
                the date hereof the reporting person has ceased to be the
                beneficial owner of more than five percent of the class of
                securities, check the following. |X|

ITEM 6          OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON:
                ---------------------------------------------------------------

                Not Applicable

ITEM 7          IDENTIFICATION AND CLASSIFICATION OF THE
                SUBSIDIARY WHICH ACQUIRED THE SECURITY BEING
                REPORTED ON BY THE PARENT HOLDING COMPANY:
                ----------------------------------------

                Not Applicable

ITEM 8          IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP:
                ----------------------------------------------------------

                Not Applicable


                                  Page 8 of 10


ITEM 9          NOTICE OF DISSOLUTION OF GROUP:
                ------------------------------

                Not Applicable

ITEM 10         CERTIFICATION:
                --------------

         By signing below the signatory certifies that, to the best of his
knowledge and belief, the securities referred to above were not acquired and are
not held for the purpose of or with the effect of changing or influencing the
control of the issuer of the securities and were not acquired and are not held
in connection with or as a participant in any transaction having that purpose or
effect.










                                  Page 9 of 10




                                    SIGNATURE

         After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

Dated:  February 14, 2006


S.A.C. CAPITAL ADVISORS, LLC


By:      /s/ Peter Nussbaum
      ---------------------------------
Name:  Peter Nussbaum
Title:  Authorized Person


S.A.C. CAPITAL MANAGEMENT, LLC


By:      /s/ Peter Nussbaum
      ---------------------------------
Name:  Peter Nussbaum
Title:  Authorized Person


SIGMA CAPITAL MANAGEMENT, LLC


By:      /s/ Peter Nussbaum
      ---------------------------------
Name:  Peter Nussbaum
Title:  Authorized Person


STEVEN A. COHEN


By:      /s/ Peter Nussbaum
      ---------------------------------
Name:  Peter Nussbaum
Title:  Authorized Person


                                  Page 10 of 10