Exhibit b.2

ALLIANZGI CONVERTIBLE & INCOME FUND II

AMENDMENT NO. 1 TO

SEVENTH AMENDED AND RESTATED BYLAWS

March 22, 2016

The following amendments to the Seventh Amended and Restated Bylaws, dated October 7, 2015 (the “Bylaws”), of AllianzGI Convertible & Income Fund II (the “Fund”) were duly adopted by resolution of a majority of the Trustees of the Fund at a meeting of the Trustees held on March 22, 2016. Any capitalized term used herein and not defined herein shall have the meaning assigned to it in the Bylaws.

1. Amendment to Section 11.1 of the Bylaws. The definition of “Fitch Criteria” in Section 11.1 of the Bylaws is hereby deleted in its entirety and replaced with the following:

“Fitch Criteria” means the Closed-End Fund Criteria Report issued by Fitch Ratings entitled “Rating Closed-End Fund Debt and Preferred Stock” dated September 16, 2015 and attached to these Bylaws as Exhibit 1, which is hereby incorporated by reference into and made a part of these Bylaws. The Trust may, but is not required to, amend or restate the Fitch Criteria from time to time, through an amendment or restatement of Exhibit 1 or otherwise, to reflect revised criteria issued by Fitch Ratings by resolution of the Board of Trustees of the Trust and without shareholder approval.

2. Amendment to Exhibit 1 to the Bylaws. Exhibit 1 to the Bylaws is hereby deleted in its entirety and replaced with Exhibit 1 attached hereto as Annex I.

ANNEX I

Exhibit 1

Fitch Criteria dated September 16, 2015