================================================================================


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


                                  SCHEDULE 13D
                                 (Rule 13d-101)
                                (Amendment No. 5)


             INFORMATION TO BE INCLUDED IN STATEMENTS FILED PURSUANT
            TO RULE 13d-1(a) AND AMENDMENTS THERETO FILED PURSUANT TO
                                  RULE 13d-2(a)


                               The Korea Fund, Inc
                               -------------------
                                (Name of Issuer)


                     Common Stock, par value $.01 per share
                     --------------------------------------
                         (Title of Class of Securities)


                                    500634100
                                 --------------
                                 (CUSIP Number)


                                 Barry M. Olliff
            c/o City of London Investment Management Company Limited
                     10 Eastcheap, London EC3M ILX, England
                                +44 207 711 0771
            --------------------------------------------------------
            (Name, Address and Telephone Number of Person Authorized
                     to Receive Notices and Communications)


                                November 12, 2004
             -------------------------------------------------------
             (Date of Event Which Requires Filing of This Statement)


If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Schedule 13D, and is filing this
schedule because of Rule 13d-1(e), (f) or (g), check the following box [_].

*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 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 or otherwise subject to the liabilities of that section of the Act but
shall be subject to all other provisions of the Act.

================================================================================

                               (Page 1 of 7 Pages)

===================                                                  ===========
CUSIP NO. 500634100                    13D                           PAGE 2 of 7
===================                                                  ===========

================================================================================
     1       NAME OF REPORTING PERSONS
             S.S. OR I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS

             City of London Investment Group PLC, a company incorporated under
             the laws of England and Wales.
------------ -------------------------------------------------------------------
     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP            (A) [_]
                                                                         (B) [_]

------------ -------------------------------------------------------------------
     3       SEC USE ONLY


------------ -------------------------------------------------------------------
     4       SOURCE OF FUNDS*

             OO
------------ -------------------------------------------------------------------
     5       CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT
             TO ITEM 2(d) OR 2(e)
                                                                             [_]
------------ -------------------------------------------------------------------
     6       CITIZENSHIP OR PLACE OF ORGANIZATION

             England and Wales
--------------------------------------------------------------------------------
  NUMBER OF              7      SOLE VOTING POWER

   SHARES                       4,426,782
                   ------------ ------------------------------------------------
BENEFICIALLY             8      SHARED VOTING POWER

  OWNED BY                      0
                   ------------ ------------------------------------------------
    EACH                 9      SOLE DISPOSITIVE POWER

  REPORTING                     4,426,782
                   ------------ ------------------------------------------------
   PERSON               10      SHARED DISPOSITIVE POWER

    WITH                        0
------------ -------------------------------------------------------------------
    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

             4,426,782
------------ -------------------------------------------------------------------
    12       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN
             SHARES
                                                                             [_]
------------ -------------------------------------------------------------------
    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

             9.90%
------------ -------------------------------------------------------------------
    14       TYPE OF REPORTING PERSON*

             HC
================================================================================

===================                                                  ===========
CUSIP NO. 500634100                    13D                           PAGE 3 of 7
===================                                                  ===========

================================================================================
     1       NAME OF REPORTING PERSONS
             S.S. OR I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS

             City of London Investment Management Company Limited, a company
             incorporated under the laws of England and Wales.
------------ -------------------------------------------------------------------
     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP            (A) [_]
                                                                         (B) [_]

------------ -------------------------------------------------------------------
     3       SEC USE ONLY


------------ -------------------------------------------------------------------
     4       SOURCE OF FUNDS*

             WC
------------ -------------------------------------------------------------------
     5       CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT
             TO ITEM 2(d) OR 2(e)
                                                                             [_]
------------ -------------------------------------------------------------------
     6       CITIZENSHIP OR PLACE OF ORGANIZATION

             England and Wales
--------------------------------------------------------------------------------
  NUMBER OF              7      SOLE VOTING POWER

   SHARES                       4,398,762
                   ------------ ------------------------------------------------
BENEFICIALLY             8      SHARED VOTING POWER

  OWNED BY                      0
                   ------------ ------------------------------------------------
    EACH                 9      SOLE DISPOSITIVE POWER

  REPORTING                     4,398,762
                   ------------ ------------------------------------------------
   PERSON               10      SHARED DISPOSITIVE POWER

    WITH                        0
------------ -------------------------------------------------------------------
    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

             4,398,762
------------ -------------------------------------------------------------------
    12       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN
             SHARES
                                                                             [_]
------------ -------------------------------------------------------------------
    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

             9.84%
------------ -------------------------------------------------------------------
    14       TYPE OF REPORTING PERSON*

             IA
================================================================================

===================                                                  ===========
CUSIP NO. 500634100                    13D                           PAGE 4 of 7
===================                                                  ===========

     This Amendment No. 5 to Schedule 13D (this "Amendment No. 5") should be
     read in conjunction with the Schedule 13D filed with the U.S. Securities
     and Exchange Commission (the "SEC") on February 17, 2004 (the "Original
     Schedule 13D"), with Amendment No. 1 to Schedule 13D filed with the SEC on
     March 1, 2004 ("Amendment No. 1"), with Amendment No. 2 to Schedule 13D
     filed with the SEC on May 5, 2004 ("Amendment No. 2"), with Amendment No. 3
     to Schedule 13D filed with the SEC on July 8, 2004 ("Amendment No. 3") and
     with Amendment No. 4 to Schedule 13D filed with the SEC on August 31, 2004
     ("Amendment No. 4" and, together with Amendment No. 1, Amendment No. 2 and
     Amendment No. 3, the "Amendments") by City of London Investment Group PLC
     and City of London Investment Management Company Limited relating to the
     shares of common stock, par value $0.01 per share (the "Shares"), of The
     Korea Fund, Inc., a Maryland corporation (the "Fund"). This Amendment No. 5
     amends Items 3, 4, 5 and 7 of the Original Schedule 13D as amended by the
     Amendments. All other information in the Original Schedule 13D and the
     Amendments remain in effect. All capitalized terms used herein and not
     otherwise defined shall have the meanings ascribed thereto in the Original
     Schedule 13D as amended by the Amendments.

ITEM 3     SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.
           -------------------------------------------------

           Item 3 is hereby amended and restated in its entirety to read as
           follows:

           The funds used to purchase the Shares described in this statement
           were acquired through open market purchases and were derived from
           EWF's, GEM's, IEM's, GFM's, FREE's and Global's investment capital
           and funds provided by the Accounts. The aggregate amount of the funds
           used to purchase all of the Shares purchased by EWF, GEM, IEM, GFM,
           FREE, Global's and the Accounts is $1,933,746, $18,788,073,
           $18,090,202, $1,822,797, $6,366,520, $489,912, and $31,933,884,
           respectively.

ITEM 4.    PURPOSE OF TRANSACTION.
           ----------------------

           Item 4 is hereby amended by adding the following:

           On November 12, 2004, CLIG sent a letter to each member of the board
           of directors of the Fund. In the letter, CLIG sets forth the minimum
           steps that CLIG believes the Fund's board of directors should take in
           order to satisfy its obligations to the Fund and the Fund's
           stockholders. The foregoing description of the letter is not intended
           to be complete and is qualified in its entirety by the complete text
           of the form of letter filed as Exhibit A hereto, which form of letter
           is incorporated herein by reference.

           Other than as set forth above, none of the Reporting Persons or, in
           the case of non-individual Reporting Persons, any of their directors
           or executive officers identified in Item 2, have any present plans or
           proposals which relate to or could result in, any of the matters


===================                                                  ===========
CUSIP NO. 500634100                    13D                           PAGE 5 of 7
===================                                                  ===========

           referred to in paragraphs (a) through (j), inclusive, of Item 4 of
           Schedule 13D (although they reserve the right to develop any such
           plans or proposals).

ITEM 5.    INTERESTS IN SECURITIES OF THE ISSUER.
           -------------------------------------

           Items 5(a) and 5(b) below are hereby amended and restated in their
           entirety and Item 5(c) is hereby amended as follows:

           (a) and (b). As of the date hereof, EWF, GEM, IEM, GFM, FREE, the
           Accounts and Global owned directly 132,036, 1,157,847, 1,118,627,
           113,436, 322,994, 1,553,822 and 28,020 Shares, respectively,
           representing approximately 0.30%, 2.59%, 2.50%, 0.25%, 0.72%, 3.47%
           and 0.06%, respectively, of the Shares outstanding (based on the most
           recent Share information publicly disclosed by the Fund).

           As of the date hereof, CLIG, through its control of CLIM and City of
           London Quantitative Management Ltd., is the beneficial owner of
           4,426,782 Shares, representing approximately 9.90% of the Shares
           outstanding (based on the most recent Share information publicly
           disclosed by the Fund)

           As of the date hereof, CLIM, through EWF, GEM, IEM, FREE, GFM and the
           Accounts, is the beneficial owner of 4,398,762 Shares, representing
           approximately 9.84% of the Shares outstanding (based on the most
           recent Share information publicly disclosed by the Fund).

           (c). Except as described below, no transactions in the Shares were
           effected by the Reporting Persons, or, to their knowledge, any of the
           persons identified in Item 2, during the past sixty days.

           During the past 60 days, the following open market purchases of
           Shares have been made by the Accounts:

           Date of Purchase
           Number of Shares Purchased
           Price Paid/Share

           November 12, 2004
           25,000
           $21.8900

           November 5, 2004
           15,700
           $21.3656

           October 7, 2004
           30,000


===================                                                  ===========
CUSIP NO. 500634100                    13D                           PAGE 6 of 7
===================                                                  ===========

           $21.6800


           During the past 60 days, the following open market sales of Shares
           have been made by IEM:

           Date of Sale
           Number of Shares Sold
           Price Received/Share

           October 7, 2004
           24,000
           $21.6800


           During the past 60 days, the following open market sales of Shares
           have been made by FREE:

           Date of Sale
           Number of Shares Sold
           Price Received/Share

           October 7, 2004
           6,000
           $21.6800


ITEM 7     MATERIALS TO BE FILED AS EXHIBITS.
           ---------------------------------

           Item 7 is hereby amended by adding the following:

           Exhibit A. Form of Letter sent to each member of the board of
           directors of The Korea Fund, Inc.


===================                                                  ===========
CUSIP NO. 500634100                    13D                           PAGE 7 of 7
===================                                                  ===========

                                    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: November 14, 2004


                                                CITY OF LONDON INVESTMENT GROUP 
                                                PLC

                                                /s/ Barry M. Olliff
                                                --------------------------------
                                                Name: Barry M. Olliff
                                                Title: Director


                                                CITY OF LONDON INVESTMENT 
                                                MANAGEMENT COMPANY LIMITED

                                                /s/ Barry M. Olliff
                                                --------------------------------
                                                Name: Barry M. Olliff
                                                Title: Director