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

                                 SCHEDULE 13G

                  UNDER THE SECURITIES EXCHANGE ACT OF 1934

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


                      Common Stock, $0.0001 par value
------------------------------------------------------------------------------
                       (Title of Class of Securities)


                                 015351109
                    -----------------------------------
                               (CUSIP Number)

                              January 28, 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 disclosures provided in a prior cover page.

The information required in 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).




-------------------------------                          ----------------------
CUSIP NO. 015351109                       13G               PAGE 2 OF 9 PAGES
-------------------------------                          ----------------------


--------- ---------------------------------------------------------------------
    1     NAMES OF REPORTING PERSONS
          I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)
                            Ziff Asset Management, L.P.
--------- ---------------------------------------------------------------------
    2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
          (SEE INSTRUCTIONS)                                    (A) |_|
                                                                (B) |_|
--------- ---------------------------------------------------------------------
    3     SEC USE ONLY
--------- ---------------------------------------------------------------------
    4     CITIZENSHIP OR PLACE OF ORGANIZATION

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

       NUMBER OF                        0

         SHARES
                        ------ ------------------------------------------------
                          6    SHARED VOTING POWER
      BENEFICIALLY
                                        1,677,773
        OWNED BY
                        ------ ------------------------------------------------
          EACH            7    SOLE DISPOSITIVE POWER

                                        0
       REPORTING
                        ------ ------------------------------------------------
         PERSON           8    SHARED DISPOSITIVE POWER
          WITH
                                        1,677,773
--------- ---------------------------------------------------------------------
    9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                   1,677,773
--------- ---------------------------------------------------------------------
    10    CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
          (SEE INSTRUCTIONS)                                        |_|
--------- ---------------------------------------------------------------------
    11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                   6.03%
--------- ---------------------------------------------------------------------
    12    TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                   PN
--------- ---------------------------------------------------------------------



-------------------------------                          ----------------------
CUSIP NO. 015351109                       13G               PAGE 3 OF 9 PAGES
-------------------------------                          ----------------------


--------- ---------------------------------------------------------------------
    1     NAMES OF REPORTING PERSONS
          I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)
                            PBK Holdings, Inc.
--------- ---------------------------------------------------------------------
    2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
          (SEE INSTRUCTIONS)                                    (A) |_|
                                                                (B) |_|
--------- ---------------------------------------------------------------------
    3     SEC USE ONLY
--------- ---------------------------------------------------------------------
    4     CITIZENSHIP OR PLACE OF ORGANIZATION

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

       NUMBER OF                        0

         SHARES
                        ------ ------------------------------------------------
                          6    SHARED VOTING POWER
      BENEFICIALLY
                                        1,677,773
        OWNED BY
                        ------ ------------------------------------------------
          EACH            7    SOLE DISPOSITIVE POWER

                                        0
       REPORTING
                        ------ ------------------------------------------------
         PERSON           8    SHARED DISPOSITIVE POWER
          WITH
                                        1,677,773
--------- ---------------------------------------------------------------------
    9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                   1,677,773
--------- ---------------------------------------------------------------------
    10    CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
          (SEE INSTRUCTIONS)                                        |_|
--------- ---------------------------------------------------------------------
    11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                   6.03%
--------- ---------------------------------------------------------------------
    12    TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                   CO
--------- ---------------------------------------------------------------------



-------------------------------                          ----------------------
CUSIP NO. 015351109                       13G               PAGE 4 OF 9 PAGES
-------------------------------                          ----------------------


--------- ---------------------------------------------------------------------
    1     NAMES OF REPORTING PERSONS
          I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)
                            Philip B. Korsant
--------- ---------------------------------------------------------------------
    2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
          (SEE INSTRUCTIONS)                                    (A) |_|
                                                                (B) |_|
--------- ---------------------------------------------------------------------
    3     SEC USE ONLY
--------- ---------------------------------------------------------------------
    4     CITIZENSHIP OR PLACE OF ORGANIZATION

                            United States of America
                        ------ ------------------------------------------------
                          5    SOLE VOTING POWER

       NUMBER OF                        0

         SHARES
                        ------ ------------------------------------------------
                          6    SHARED VOTING POWER
      BENEFICIALLY
                                        1,677,773
        OWNED BY
                        ------ ------------------------------------------------
          EACH            7    SOLE DISPOSITIVE POWER

                                        0
       REPORTING
                        ------ ------------------------------------------------
         PERSON           8    SHARED DISPOSITIVE POWER
          WITH
                                        1,677,773
--------- ---------------------------------------------------------------------
    9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                   1,677,773
--------- ---------------------------------------------------------------------
    10    CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
          (SEE INSTRUCTIONS)                                        |_|
--------- ---------------------------------------------------------------------
    11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                   6.03%
--------- ---------------------------------------------------------------------
    12    TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                   IN
-------------------------------------------------------------------------------


                                                              Page 5 of 9 Pages

 

ITEM 1. (A)    NAME OF ISSUER
 
Alexion Pharmaceuticals, Inc.
 
ITEM 1. (B)    ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES

352 Knotter Drive
Cheshire, CT  06410

ITEM 2. (A)    NAME OF PERSON FILING

This  Schedule 13G is being filed on behalf of the  following  persons (the
"Reporting Persons")*:

(i)     Ziff Asset Management, L.P. ("ZAM");
(ii)    PBK Holdings, Inc. ("PBK"); and
(iii)   Philip B. Korsant

*       Attached as Exhibit A is a copy of an agreement among the Reporting
Persons that this Schedule 13G is being filed on behalf of each of them.

ITEM 2. (B)    ADDRESS OF PRINCIPAL BUSINESS OFFICE OR, IF NONE, RESIDENCE

Ziff Asset Management, L.P.
283 Greenwich Avenue
Greenwich, CT  06830

PBK Holdings, Inc.
283 Greenwich Avenue
Greenwich, CT  06830

Philip B. Korsant
283 Greenwich Avenue
Greenwich, CT  06830

ITEM 2. (C)    CITIZENSHIP

See Item 4 of the attached cover pages.

ITEM 2. (D)    TITLE OF CLASS OF SECURITIES

Common Stock, $0.0001 par value

ITEM 2. (E)    CUSIP NUMBER

015351109

ITEM 3.

Not applicable as this Schedule 13G is filed pursuant to Rule 13d-1(c).



                                                              Page 6 of 9 Pages

ITEM 4. OWNERSHIP

(a)     Amount beneficially owned:

        See Item 9 of the attached cover pages.

(b)     Percent of class:

        See Item 11 of the attached cover pages.

(c)     Number of shares as to which such person has:
 
        (i)    Sole power to vote or to direct the vote:
 
               See Item 5 of the attached cover pages.

        (ii)   Shared power to vote or to direct the vote:
 
               See Item 6 of the attached cover pages.

        (iii)  Sole power to dispose or to direct the disposition:
 
               See Item 7 of the attached cover pages.

        (iv)   Shared power to dispose or to direct the disposition:
 
               See Item 8 of the attached cover pages.

ITEM 5.        OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS
 
Not Applicable.

ITEM 6.        OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON
 
Philip B. Korsant shares voting and dispositive power over the shares of
Common Stock that he beneficially owns with ZAM, the owner of record of the
shares of Common Stock. PBK also shares voting and dispositive power over
the shares of Common Stock that it beneficially owns with ZAM.

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.


ITEM 9.        NOTICE OF DISSOLUTION OF GROUP
 
Not Applicable.



                                                              Page 7 of 9 Pages

ITEM 10.       CERTIFICATION
 
By signing below I certify that, to the best of my 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 8 of 9 Pages

                                 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 4, 2005

                                        ZIFF ASSET MANAGEMENT, L.P.
                                        By: PBK Holdings, Inc., its general
                                            partner


                                        By: /s/ DAVID GRAY
                                            ------------------------------------
                                            Name:  David Gray
                                            Title: Vice President


                                        PBK HOLDINGS, INC.


                                        By: /s/ DAVID GRAY
                                            ------------------------------------
                                            Name:  David Gray
                                            Title: Vice President



                                            /s/ PHILIP B. KORSANT
                                            ------------------------------------
                                                   Philip B. Korsant