<PAGE>

EXHIBIT 10.4


                               THIRD AMENDMENT TO THE
               AMENDED AND RESTATED AGREEMENT OF LIMITED PARTNERSHIP
                             OF GREAT LAKES REIT, L.P.


     This Third Amendment to the Amended and Restated Agreement of Limited
Partnership of Great Lakes REIT, L.P. (the "Third Amendment") is made and
entered into as of the 22nd day of May, 1998 by Great Lakes REIT, Inc., a
Maryland corporation ("GLREIT").

RECITALS:

     WHEREAS, GLREIT is the sole general partner of a Delaware limited
partnership known as Great Lakes REIT, L.P. (the "Partnership"), the business
and affairs of which are conducted in accordance with the terms and conditions
of a certain Agreement of Limited Partnership dated September 27, 1996, as
amended and restated by the Amended and Restated Agreement of Limited
Partnership dated as of December 19, 1996, the First Amendment to the Amended
and Restated Agreement of Limited Partnership of Great Lakes REIT, L.P. dated
February 6, 1997 (collectively the "Partnership Agreement"); and the Second
Amendment to the Amended and Restated Agreement of Limited Partnership of Great
Lakes REIT, L.P. dated February 10, 1997 (collectively the "Partnership
Agreement");

     WHEREAS, Section 13.1(b)(ii) of the Partnership Agreement expressly
provides, that GLREIT, the general partner of the Partnership shall amend the
Partnership Agreement to reflect the admission of Partners in conformance with
the Partnership Agreement;

     WHEREAS, the individuals listed in Exhibit A attached hereto (the
"Contributing Partners") have contributed interests in certain real estate to
the Partnership in consideration for Limited Partnership interests; and

     WHEREAS, GLREIT as general partner of the Partnership desires to amend the
Partnership Agreement to reflect the addition of the Contributing Partners to
the Partnership as new Limited Partners and to revise the percentage interests
of the Partners to reflect the new interests;

     NOW THEREFORE, the parties hereto hereby agree as follows:

     5.   The Contributing Partners identified in Exhibit A attached hereto are
          hereby added to the Partnership as new Limited Partners and the
          Percentage Interests of the Partners are hereby revised as noted in
          Exhibit A attached.

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     6.   Except as set forth above, no other provision of the Partnership
          Agreement shall be affected, amended or modified except to the extent
          necessary to conform to the above amendment.  Unless defined herein
          all capitalized terms used herein shall have the definition provided
          in the Partnership Agreement.

     7.   The foregoing amendment has been proposed by GLREIT, in its capacity
          as the General Partner of the Partnership in accordance with the
          provisions of Section 13.1(b)(ii) of the Partnership Agreement.

     IN WITNESS WHEREOF, the parties hereto have executed this Third Amendment
as of the date and year first above written.

                                        GREAT LAKES REIT, INC.



                                        By:    James Hicks
                                           -----------------------------------
                                               James Hicks
                                        Its:   Vice President

<PAGE>

                                  EXHIBIT A TO THE
                                AMENDED AND RESTATED
                          AGREEMENT OF LIMITED PARTNERSHIP
                                         OF
                               GREAT LAKES REIT, L.P.
                                          
                                          
                            EFFECTIVE DATE: May 22, 1998

<TABLE>
<CAPTION>

                                                          Partnership       Preferred       Percentage 
 Name and Address             Capital Contribution        Units             Units           Interest
 ----------------             --------------------        -----------       ---------       ----------
<S>                           <C>                         <C>               <C>             <C>
 GENERAL PARTNER:

 Great Lakes REIT, Inc.       Real estate  and cash       8,652,368.5                         49.7889%
 823 Commerce Drive                                                                                    
 Oak Brook, IL  60523                                                                                  
                                                                                                       
 LIMITED PARTNERS:                                                                                     
                                                                                                       
 Great Lakes REIT, Inc.       Real estate and cash        8,652,368.5                         49.7889%
 823 Commerce Drive                                                                                    
 Oak Brook, IL  60521                                                                                  
 GLR No. 3                    Cash                                881                          0.0051%
 823 Commerce Drive                                                                                    
 Oak Brook, IL  60523                                                                                  
 FCL Mackey                   Elgin Indust. JV Units           24,050                          0.1384%
 George F. Beardsley          Real estate (Inverness)          16,149                          0.0929%
 Clay L. Boelz                Real estate (Inverness)          16,149                          0.0929%
 John F. O'Meara              Real estate (Inverness)          16,149                          0.0929%
                                                               ------                          -------
 Total:                                                    17,378,115                        100.0000%
</TABLE>