<Page>

                                                                    EXHIBIT 10.6

                                  AMENDMENT TO
                           RESTRICTED SHARE AGREEMENT

     THIS AMENDMENT to Restricted Share Agreement is made as of the 1st day of
July, 2002, between Corporate Office Properties Trust, a Maryland business trust
(the "Company") and Roger A. Waesche, Jr. (the "Employee").

                                    RECITALS

     A.   The Company and the Employee entered into a Restricted Share Agreement
on July 2, 2001 (the "Agreement") providing for the issuance of 23,000 common
shares (the "Restricted Shares") of beneficial interest, $0.01 par value per
share, of the Company pursuant to the Corporate Office Properties Trust 1998
Long Term Incentive Plan (the "Plan").

     B.   The Restricted Shares were subject to certain restrictions on the
beneficial ownership of the shares as specified in the Agreement.

     C.   Pursuant to Paragraph 8(d) of the Plan, the terms of an award of
Restricted Shares under the Plan may be amended with the consent of the
Employee.

     D.   The Employee and the Company wish to amend the Agreement as
hereinafter provided in connection with a renegotiation of an employment
agreement between the Company and the Employee.

     NOW, THEREFORE, in consideration of the foregoing, the Company and the
Employee hereby amend the Agreement as follows, effective as of July 1, 2002:

     1.   Section 2(b) of the Agreement is amended by deleting the schedule
referenced therein in its entirety and substituting, therefore, the following:

<Table>
<Caption>
                                 Percentage of Total                  Amount of Total
                                Number of Restricted               Number of Restricted
                                 Shares as to Which                 Shares as to Which
          Date              Forfeiture Restricted Lapse        Forfeiture Restrictions Lapse
          ------------      ---------------------------        -----------------------------
          <S>                       <C>                                      <C>
          July 2, 2002                   0%                                      0
          July 2, 2003              33 1/3%                                  7,666
          July 2, 2004              33 1/3%                                  7,667
          July 2, 2005              33 1/3%                                  7,667
</Table>

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     Except as herein expressly changed, the Agreement is ratified and confirmed
in all respects.

     IN WITNESS WHEREOF, the Company and Employee have executed this Amendment
the ___ day of ___________, 2002.


EMPLOYEE                            CORPORATE OFFICE
                                    PROPERTIES TRUST


                                    By:/s/ Clay W. Hamlin, III
- ------------------------------         -----------------------------------------
Roger A. Waesche, Jr.

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