SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

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                                    FORM 6-K

                        REPORT OF FOREIGN PRIVATE ISSUER
                    PURSUANT TO RULE 13A-16 OR 15D-16 OF THE
                         SECURITIES EXCHANGE ACT OF 1934


For the month of: May 2004
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Commission File Number: 333-103019
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                        Geac Computer Corporation Limited
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                 (Translation of registrant's name into English)

         11 Allstate Parkway, Suite 300, Markham, Ontario L3R9T8 Canada
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                    (Address of principal executive offices)


Indicate by check mark whether the registrant files or will file annual reports
under cover Form 20-F or Form 40-F. Form 20-F....X..... Form 40-F.........

Indicate by check mark if the registrant is submitting the Form 6-K in paper as
permitted by Regulation S-T Rule 101(b)(1): ____

Note: Regulation S-T Rule 101(b)(1) only permits the submission in paper of a
Form 6-K if submitted solely to provide an attached annual report to security
holders.

Indicate by check mark if the registrant is submitting the Form 6-K in paper as
permitted by Regulation S-T Rule 101(b)(7): ____

Note: Regulation S-T Rule 101(b)(7) only permits the submission in paper of a
Form 6-K if submitted to furnish a report or other document that the registrant
foreign private issuer must furnish and make public under the laws of the
jurisdiction in which the registrant is incorporated, domiciled or legally
organized (the registrant's "home country"), or under the rules of the home
country exchange on which the registrant's securities are traded, as long as the
report or other document is not a press release, is not required to be and has
not been distributed to the registrant's security holders, and, if discussing a
material event, has already been the subject of a Form 6-K submission or other
Commission filing on EDGAR.

Indicate by check mark whether by furnishing the information contained in this
Form, the registrant is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

Yes ..... No ..X...

If "Yes" is marked, indicate below the file number assigned to the registrant in
connection with Rule 12g3-2(b): 82- ________



     On May 4, 2004, Geac Computer Corporation Limited filed on the SEDAR
website maintained by the Canadian Depository for Securities Limited at
www.sedar.com a press release issued on May 4, 2004, a copy of which is attached
as Exhibit 99.1 to this Report of Foreign Private Issuer on Form 6-K.


                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.


                                   GEAC COMPUTER CORPORATION LIMITED

                                   /s/  Jeffrey M. Snider
                                   -----------------------------------------
                                   Jeffrey M. Snider
                                   Senior Vice President and
                                   General Counsel


Date: May 4, 2004



                                  EXHIBIT INDEX

Number                        Title
- ------                        -----

99.1           Press Release issued on May 4, 2004