<PAGE>   1

                                                                    EXHIBIT 10.4

NEITHER THIS PROMISSORY NOTE NOR THE SHARES OF CAPITAL STOCK ISSUABLE HEREUNDER
HAS BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED. NO SALE OR
DISPOSITION MAY BE EFFECTED EXCEPT IN COMPLIANCE WITH RULE 144 UNDER SAID ACT OR
AN EFFECTIVE REGISTRATION STATEMENT RELATED THERETO OR AN OPINION OF COUNSEL FOR
THE HOLDER, SATISFACTORY TO THE COMPANY, THAT SUCH REGISTRATION IS NOT REQUIRED
UNDER THE ACT OR RECEIPT OF A NO-ACTION LETTER FROM THE SECURITIES AND EXCHANGE
COMMISSION.


                                 PROMISSORY NOTE


$3,000,000
8% p.a.                                                        December 21, 1999


        For value received, OMNIS TECHNOLOGY CORPORATION, a Delaware
corporation, whose principal place of business is 981 Industrial Way, San
Carlos, California 94070-4117 ("Maker"), hereby promises to pay to the order of
ASTORIA CAPITAL PARTNERS, L.P., a California limited partnership, ("Payee"), at
its principal place of business, 6600 92nd Avenue S.W., Suite ____, Portland,
Oregon 97223, or at such other place as Payee may from time specify, the
principal sum of THREE MILLION DOLLARS ($3,000,000) or so much thereof as may be
advanced and be outstanding hereunder plus interest thereon, in legal and lawful
money of the United States of America.

        This Note is made pursuant to that certain Credit Facility Agreement by
and between Maker and Payee dated as of the date hereof (the "Credit Facility
Agreement"), as amended from time to time, the terms of which are incorporated
herein by reference. Additional terms of this Note, including, without
limitation, the rate of interest, default rate of interest, terms of repayment,
security, terms of default, governing law and venue and costs and attorneys'
fees are set forth in the Credit Facility Agreement.

        Maker hereby waives diligence, demand, presentment for payment, notice
of non-payment, protest and notice of protest, and specifically consents to and
waives notice of any renewals or extensions of this Note, whether made to or in
favor of Maker or any other person or persons. The pleading of any statute of
limitations as a defense to any demand against Maker is expressly waived by each
and all of said parties to the fullest extent permitted by law. The rights,
powers and remedies of Payee under this Note shall be in addition to all rights,
powers and remedies given to Payee by virtue of any statute or rule of law,
including but not limited to the California Commercial Code. All such rights,
powers and remedies shall be cumulative and may be exercised successively or
concurrently in Payee's sole discretion. Any forbearance, failure or delay by
Payee in exercising any right, power or remedy shall not preclude further
exercise thereof, and every right, power or remedy of Payee shall continue in
full force and effect until such right, power or remedy is specifically waived
in a writing executed by Payee.



<PAGE>   2

        Notwithstanding the legend at the top of this Note, the Maker
acknowledges that a transfer of this Note or a fractional portion of this Note
to one or more of the partners who comprise Payee as a distribution without
consideration (whether upon liquidation of Payee or a withdrawal of capital by
such a partner in accordance with Payee's agreement of limited partnership) will
not require registration of this Note, any opinion of counsel for the Payee, or
any consent of the Maker.

        IN WITNESS WHEREOF, this Note has been executed and delivered as of the
date first above written by the duly authorized representative of Maker.

                                            OMNIS TECHNOLOGY CORPORATION,
                                            A DELAWARE CORPORATION




                                            By:  /s/ JAMES DORST
                                               ---------------------------------
                                            Name:  JAMES DORST
                                                 -------------------------------
                                            Title: CFO/COO
                                                  ------------------------------


                                        2