GLIATECH INC.



                            23420 COMMERCE PARK ROAD



                                 CLEVELAND, OHIO



                                  May 29, 2000



American Stock Transfer & Trust Company

40 Wall Street

New York, New York 10005

Attention:    Barry Rosenthal



                     Re: Amendment No. 2 to Rights Agreement

                         -----------------------------------



Ladies and Gentlemen:



         Pursuant to Section 27 of the Rights Agreement (the "Rights

Agreement"), dated as of July 1, 1997, as amended November 17, 1999, between

Gliatech Inc. (the "Company") and American Stock Transfer & Trust Company, as

rights agent, the Company, by resolution adopted by its Directors, hereby amends

the Rights Agreement as follows:



         1. Section 1(j) of the Rights Agreement is hereby amended and restated

in its entirety as follows:



         (j)      "Expiration Date" means the earliest of (i) the Close of

                  Business on the Final Expiration Date, (ii) the time at which

                  the Rights are redeemed as provided in Section 23, (iii) the

                  time at which all exercisable Rights are exchanged as provided

                  in Section 24, and (iv) immediately prior to the Effective

                  Time (as defined in the Merger Agreement."



         2. Section 1(a) of the Rights Agreement is hereby amended by adding the

following new Section 1(ff) at the end of such Section:



         (ff)     "Merger Agreement" means the Agreement and Plan of Merger,

                  dated as of May 29, 2000, among the Company, St. John

                  Development Corp., a Delaware corporation ("Merger Co.") and

                  Guilford Pharmaceuticals Inc., a Delaware corporation

                  ("Acquiror").



         3. Section 1 of the Rights Agreement is hereby amended by adding the

following new paragraph at the end of that Section:



                           Notwithstanding anything in this Agreement to the

                  contrary, none of Acquiror, Merger Co., any of their

                  Affiliates or Associates or any of their permitted assignees

                  or transferees shall be deemed an Acquiring Person and none

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