EXHIBIT 3.4 CERTIFICATE OF AMENDMENT OF BY-LAWS OF NEUROCRINE BIOSCIENCES, INC. (A DELAWARE CORPORATION) On May 28, 2004 the Board of Directors of Neurocrine Biosciences, Inc. approved the amendment of Section 3.2 of the By-Laws of the corporation to read as follows: 3.2 Number of Directors. The Board of Directors shall consist of eight (8) members. The number of Directors may be changed by an amendment to this by-law adopted by the Board of Directors or by the stockholders or by a duly adopted amendment to the certificate of incorporation. The Directors shall be divided into three classes, with the term of office of the first class (Class I Directors), which will initially consist of three Directors, to expire at the 2006 Annual Meeting of Shareholders; the term of office of the second class (Class II Directors), which will initially consist of three (3) Directors, to expire at the 2008 Annual Meeting of Shareholders; the term of office of the third class (Class III Directors), which will initially consist of two (2) Directors, to expire at the 2005 Annual Meeting of Shareholders; and thereafter for each such term to expire at each third succeeding Annual Meeting of Shareholders held after such election.