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

                          FORM N-CSR/A

       CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT
                       INVESTMENT COMPANIES

Investment Company Act file number:         811-10533

Exact name of registrant as specified
in charter:                                 Reserve Municipal Money Market Trust

Address of principal executive offices:     1250 Broadway
                                            New York, NY 10001-3701

Name and address of agent for service:      Amy W. Bizar
                                            1250 Broadway
                                            New York, NY 10001-3701

Registrant's telephone number, including
area code:                                  212-401-5500

Date of fiscal year end:                    May 31

Date of reporting period:                   May 31, 2004


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     The sole purpose of this amendment is to furnish the certification
required by Section 906 of the Sarbanes-Oxley Act of 2002 (Subsections (a)
and (b) of Section 1350, Chapter 63 of Title 18, United States Code) which
was omitted from the Form N-CSR filed by the Registrant with the Securities
and Exchange Commission on August 9, 2004.

ITEM 12. EXHIBITS.

     Certification of chief executive officer and chief financial officer
pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 is attached as
Exhibit 99.906CERT.

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                                  SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934 and
the Investment Company Act of 1940, the registrant has duly caused this
report to be signed on its behalf by the undersigned, thereunto duly
authorized.

Reserve Municipal Money Market Trust


By: /s/ Bruce R. Bent
    -----------------------
    Name:  Bruce R. Bent
    Title: Chairman and CEO

Date:  January 24, 2005

     Pursuant to the requirements of the Securities Exchange Act of 1934 and
the Investment Company Act of 1940, this report has been signed by the
following persons on behalf of the registrant and in the capacities and on
the dates indicated.

By: /s/ Bruce R. Bent
    -----------------------
    Name:  Bruce R. Bent
    Title: Chairman and CEO

Date:  January 24, 2005


By: /s/ Arthur T. Bent III
    -----------------------
    Name:  Arthur T. Bent III
    Title: Treasurer (Principal Financial Officer)

Date:  January 24, 2005