EXHIBIT 3.4

AMENDMENT TO BYLAWS

OF

INFINITY PHARMACEUTICALS, INC.

The Bylaws of Infinity Pharmaceuticals, Inc.,
as amended to date (the Bylaws), are hereby further amended as follows:

1. Article III, Section 1 of the Bylaws is deleted
in its entirety and replaced with the following:

Section 1. Number, Term of Office and Qualification. The term of office
of each Director who is in office immediately prior to the closing of the polls for the election of Directors at the 2008 annual meeting of stockholders shall expire at such time. From and after the 2008 annual meeting of stockholders, each Director
shall be elected to hold office for a term of one year, until the next annual meeting of stockholders and until such persons successor is duly elected and qualified, subject to his or her earlier death, resignation or removal from the board of
directors. Directors need not be stockholders. The number of Directors which shall constitute the whole Board shall be established by the Board of Directors.

2. Article III, Section 13 of the Bylaws is deleted in its entirety and replaced with the following:

Section 13. Removal. Subject to any limitations imposed by law or the Certificate of Incorporation, as amended from time to time, the Board of Directors, or any individual Director, may be removed from office at any time
with or without cause by the affirmative vote of the holders of at least a majority of the outstanding shares entitled to vote at an election of Directors.

3. Article X, Sections 1(b) and 1(c) are deleted in their entirety and replaced with the following:

(b) Notwithstanding any other provisions of these Bylaws or any provision of law which might otherwise permit a lesser vote or no vote, but in addition to any affirmative vote of the holders of any particular class or series of the
Voting Stock required by law, the Certificate of Incorporation, as amended from time to time, or any Preferred Stock Designation (as the term is defined in the Certificate of Incorporation, as amended), the affirmative vote of the holders of at
least sixty-six and two-thirds percent (66-2/3%) of the voting power of all of the then-outstanding shares of the Voting Stock, voting together as a single class, shall be required to alter, amend or repeal this paragraph (b) or Section 2,
Section 5 or Section 10 of Article II of these Bylaws.

(c) Notwithstanding any other provisions of these Bylaws
or any provision of law which might otherwise permit a lesser vote or no vote, but in addition to any affirmative vote of the holders of any particular class or series of the Voting Stock required by law, the Certificate of Incorporation, as amended
from time to time, or any Preferred Stock Designation (as the term is defined in the Certificate of Incorporation, as amended from time to time), the affirmative vote of at least sixty-six and two-thirds percent (66-2/3%) of the Directors, shall be
required to alter, amend or repeal this paragraph (c) or Section 2, Section 5 or Section 10 of Article II of these Bylaws.

Except as aforesaid, the Bylaws shall remain in full force and effect.



| |  |  |  |                                             
| |  |  |  | --------------------------------------------
| |  |  |  | Adopted by the Board of Directors on        
| |  |  |  | March 13, 2007.                             
| |  | 
| |  |  |  | Adopted by the Stockholders on May 30, 2007.