AMENDMENT OF BIOCRYST

Exhibit 4.2

AMENDMENT OF BIOCRYST

RIGHTS AGREEMENT

1. Clause (2) of the definition of “Acquiring Person” in the Company’s Rights Agreement dated June 17, 2002 (the “Rights Agreement”), is hereby amended to read in full as follows:

“(2) William W. Featheringill (the “Permitted Investor”) or any of his Affiliates or Associates (collectively with the Permitted Investor, the “Investor Group”) to the extent that the members of the Investor Group shall become the Beneficial Owner of, in the aggregate, up to, but not exceeding, 19.9% of the shares of Common Stock of the Company then outstanding, or (3) Baker Bros. Advisors, LLC (the “Baker Permitted Investor”) or any of its Affiliates or Associates, or any entities managed by Baker Bros. Advisors, LLC, including, but not limited to, Baker Bros. Investments, L.P., Baker Bros. Investments II, L.P., Baker/Tisch Investments, L.P., Baker Biotech Fund I, L.P., 14159, L.P. and Baker Brothers Life Sciences, L.P. (collectively with the Baker Permitted Investor, the “Baker Investor Group”) to the extent that the members of the Baker Investor Group shall become the Beneficial Owner of, in the aggregate, up to, but not exceeding, 25.0% of the shares of Common Stock of the Company then outstanding.”

2. In the two places where the following parenthetical appears in clause (i) of the definition of “Acquiring Person” in the Rights Agreement:

“(or, in the case of the Investor Group, more than 19.9% of the shares of Common Stock of the Company then outstanding)”

it shall be amended to read in full as follows:

“(or, in the case of the Investor Group or the Baker Investor Group, respectively, more than 19.9% or 25%, respectively, of the shares of Common Stock of the Company then outstanding)”.

3. References to the “Rights Agreement between BioCryst Pharmaceuticals, Inc. and American Stock Transfer & Trust Company, dated as of June 14, 2002” shall be amended to refer to the “Rights Agreement between BioCryst Pharmaceuticals, Inc. and American Stock Transfer & Trust Company, dated as of June 14, 2002, as amended to date.”