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



                                  SCHEDULE 13G

                   Under the Securities Exchange Act of 1934*

                                (Amendment No. 4)

                         Core-Mark Holding Company, Inc.
                         -------------------------------
                                (Name of Issuer)

                     Common Stock, par value $0.01 per share
                     ---------------------------------------
                         (Title of Class of Securities)

                                    218681104
                                    ---------
                                 (CUSIP Number)

                                December 31, 2008
                                -----------------
             (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 (the "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.  218681104                    13G               Page 2 of 8 Pages
----------------------------                              ----------------------

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

           Third Point 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       6      SHARED VOTING POWER
      SHARES
   BENEFICIALLY             625,000
     OWNED BY
       EACH          ------ ----------------------------------------------------
     REPORTING       7      SOLE DISPOSITIVE POWER
      PERSON
       WITH                 0
                     ------ ----------------------------------------------------
                     8      SHARED DISPOSITIVE POWER

                            625,000
---------- ---------------------------------------------------------------------
9          AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           625,000
---------- ---------------------------------------------------------------------
10         CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

           N/A
---------- ---------------------------------------------------------------------
11         PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

           5.82%
---------- ---------------------------------------------------------------------
12         TYPE OF REPORTING PERSON

           OO
---------- ---------------------------------------------------------------------





----------------------------                              ----------------------
CUSIP No.  218681104                    13G               Page 3 of 8 Pages
----------------------------                              ----------------------

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

           Daniel S. Loeb
---------- ---------------------------------------------------------------------
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       6      SHARED VOTING POWER
      SHARES
   BENEFICIALLY             625,000
     OWNED BY
       EACH          ------ ----------------------------------------------------
     REPORTING       7      SOLE DISPOSITIVE POWER
      PERSON
       WITH                 0
                     ------ ----------------------------------------------------
                     8      SHARED DISPOSITIVE POWER

                            625,000
---------- ---------------------------------------------------------------------
9          AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           625,000
---------- ---------------------------------------------------------------------
10         CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

           N/A
---------- ---------------------------------------------------------------------
11         PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

           5.82%
---------- ---------------------------------------------------------------------
12         TYPE OF REPORTING PERSON

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








----------------------------                              ----------------------
CUSIP No.  218681104                    13G               Page 4 of 8 Pages
----------------------------                              ----------------------

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

           Third Point Offshore Fund, Ltd.
---------- ---------------------------------------------------------------------
2          CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
                                                                        (b) [X]
---------- ---------------------------------------------------------------------
3          SEC USE ONLY
---------- ---------------------------------------------------------------------
4          CITIZENSHIP OR PLACE OF ORGANIZATION

           Cayman Islands
-------------------- ------ ----------------------------------------------------
                     5      SOLE VOTING POWER

                            0
                     ------ ----------------------------------------------------
     NUMBER OF       6      SHARED VOTING POWER
      SHARES
   BENEFICIALLY             499,500
     OWNED BY
       EACH          ------ ----------------------------------------------------
     REPORTING       7      SOLE DISPOSITIVE POWER
      PERSON
       WITH                 0
                     ------ ----------------------------------------------------
                     8      SHARED DISPOSITIVE POWER

                            499,500
---------- ---------------------------------------------------------------------
9          AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           499,500
---------- ---------------------------------------------------------------------
10         CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

           N/A
---------- ---------------------------------------------------------------------
11         PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

           4.65%
---------- ---------------------------------------------------------------------
12         TYPE OF REPORTING PERSON

           OO
---------- ---------------------------------------------------------------------







     This Amendment No. 4 to Schedule 13G (this "Amendment No. 4") is being
filed with respect to the Common Stock of Core-Mark Holding Company, Inc., a
corporation organized under the laws of the State of Delaware (the "Company"),
to amend the Schedule 13G filed on February 13, 2006 (as amended by Amendment
No. 1 thereto filed on February 13, 2007, Amendment No. 2 thereto filed on
August 13, 2007, and Amendment No. 3 thereto filed on February 13, 2008, the
"Schedule 13G"). This Amendment No. 4 is being filed to disclose that the
Offshore Fund no longer beneficially owns more than 5% of the Common Stock.
Capitalized terms used herein and not otherwise defined have the meanings
ascribed in the Schedule 13G.

Item 4:   Ownership:
------    ---------

     Item 4 is hereby amended and restated as follows:

     The beneficial ownership of Common Stock by the Reporting Persons, as of
the date hereof, is as follows:

  A. Third Point LLC
     ---------------
     (a) Amount beneficially owned: 625,000
     (b) Percent of class: 5.82%. The percentages used herein and in the rest of
this Schedule 13G are calculated based upon the 10,737,663 shares of Common
Stock issued and outstanding as of September 30, 2008, as reported in the
Company's Quarterly Report on Form 10-Q for the quarterly period ended September
30, 2008.
     (c) Number of shares as to which such person has:
          (i)   Sole power to vote or direct the vote: 0
          (ii)  Shared power to vote or direct the vote: 625,000
          (iii) Sole power to dispose or direct the disposition: 0
          (iv)  Shared power to dispose or direct the disposition: 625,000

  B. Daniel S. Loeb
     --------------
     (a) Amount beneficially owned: 625,000
     (b) Percent of class: 5.82%.
     (c) Number of shares as to which such person has:
          (i)   Sole power to vote or direct the vote: 0
          (ii)  Shared power to vote or direct the vote: 625,000
          (iii) Sole power to dispose or direct the disposition: 0
          (iv)  Shared power to dispose or direct the disposition: 625,000

  C. Third Point Offshore Fund, Ltd.
     -------------------------------
     (a) Amount beneficially owned: 499,500
     (b) Percent of class: 4.65%.
     (c) Number of shares as to which such person has:
          (i)   Sole power to vote or direct the vote: 0
          (ii)  Shared power to vote or direct the vote: 499,500
          (iii) Sole power to dispose or direct the disposition: 0
          (iv)  Shared power to dispose or direct the disposition: 499,500




Item 10:  Certification:
-------   -------------

     Each of the Reporting Persons hereby makes the following certification:

     By signing below, the undersigned certifies that, to the best of its
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.


                         [Signatures on following page]















                                    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:  January 6, 2009



                              THIRD POINT LLC

                              By: Daniel S. Loeb, Chief Executive Officer


                              By:       /s/ William Song
                                        ----------------------------------------
                              Name:     William Song
                              Title:    Attorney-in-Fact



                              THIRD POINT OFFSHORE FUND, LTD.

                              By: Daniel S. Loeb, Director


                              By:       /s/ William Song
                                        ----------------------------------------
                              Name:     William Song
                              Title:    Attorney-in-Fact


                              DANIEL S. LOEB


                              By:       /s/ William Song
                                        ----------------------------------------
                              Name:     William Song
                              Title:    Attorney-in-Fact





               [SIGNATURE PAGE TO AMENDMENT NO. 4 TO SCHEDULE 13G
                WITH RESPECT TO CORE-MARK HOLDING COMPANY, INC.]














                                  EXHIBIT INDEX
                                  -------------

Exhibit 99.2:  Power of Attorney granted by Daniel S. Loeb in favor of James P.
               Gallagher, William Song, Joshua L. Targoff and Bruce Wilson,
               dated June 12, 2008, was previously filed with the SEC on
               September 9, 2008 as an exhibit to Amendment No. 4 to Schedule
               13D filed by Third Point LLC, Third Point Offshore Fund, Ltd. and
               Daniel S. Loeb with respect to Flow International Corporation and
               is incorporated herein by reference.