Exhibit (b)(2)

AMENDMENT NO. 1

TO

AMENDED AND RESTATED BYLAWS

OF

THE GABELLI CONVERTIBLE AND INCOME SECURITIES FUND INC.

Effective: February 22, 2018

On February 22, 2018, the Board of Directors of The Gabelli Convertible and Income Securities Fund Inc. (the “Fund”), in accordance with the Fund’s Amended and Restated Bylaws (the “Bylaws”) and the Maryland General Corporation Law, approved and adopted the following amendment to the Bylaws, to be effective immediately:

The first sentence of Article III, Section II of the Bylaws is hereby deleted in its entirety, and the following sentence is hereby substituted in lieu thereof:

“The number of directors shall be fixed from time to time by resolution of the Board of Directors adopted by a majority of the directors then in office; provided, however, that the number of directors shall in no event be fewer than the minimum number required by the MGCL nor more than thirteen (13).”