PUTNAM INVESTMENT GRADE MUNICIPAL TRUST II

                            Amendment No. 2 to Bylaws

         WHEREAS, Article 13, Section 13.1 and Article 12, Section 12.1, Part
I, paragraph 6(c) of the Bylaws (the "Bylaws") of Putnam Investment Grade
Municipal Trust II (the "Trust") permit the Trustees of the Trust (the
"Trustees") to amend, alter or repeal the definitions of certain listed terms
contained in the Bylaws, subject to written confirmation from Moody's
Investors Service, Inc. ("Moody's") and Standard & Poors ("S&P") that such
amendment, alteration or repeal will not affect the ratings then assigned to
the Trust's outstanding Remarketed Preferred Shares ("Preferred Shares"), and
to amend, alter or repeal any other provision of the Bylaws provided that
such amendment, alteration or repeal does not materially and adversely affect
any preference, right or power of the Preferred Shares or any holder thereof;

         WHEREAS, the Trustees desire to amend the Bylaws so as to eliminate
the liquidity test contained in Article 12, Section 12.1, Part I, paragraph 9
of the Bylaws;

         WHEREAS, Moody's and S&P have confirmed to the Trust that the
deletion of the definitions of the terms "Dividend Coverage Amount,"
"Dividend Coverage Assets" and "Minimum Liquidity Level" will not impair
their ratings of outstanding Preferred Shares; and

         WHEREAS, the Trustees have determined that, in the event that the
definitions of the terms "Dividend Coverage Amount," "Dividend Coverage
Assets" and "Minimum Liquidity Level" are deleted, the deletion of Article
12, Section 12.1, Part I, paragraphs 8(g)(ii)(b) and 9 of the Bylaws would
not materially and adversely affect any preference, right or power of the
Preferred Shares or any holder thereof;

         NOW, THEREFORE, the Bylaws are hereby amended as follows:

1.       ARTICLE 12, SECTION 12.1, PART I, PARAGRAPH 1 OF THE BYLAWS IS HEREBY
         AMENDED BY DELETING THE DEFINITIONS OF THE TERMS "DIVIDEND COVERAGE
         AMOUNT," "DIVIDEND COVERAGE ASSETS" AND "MINIMUM LIQUIDITY LEVEL" SET
         FORTH THEREIN;

2.       ARTICLE 12, SECTION 12.1, PART I, PARAGRAPH 8(g)(ii)(b) IS HEREBY
         DELETED AND ARTICLE 12, SECTION 12.1, PART I, PARAGRAPH 8(g)(ii)(c) IS
         HEREBY REDESIGNATED ARTICLE 12, SECTION 12.1, PART I, PARAGRAPH
         8(g)(ii)(b); AND

3.       THE TEXT OF ARTICLE 12, SECTION 12.1, PART I, PARAGRAPH 9 OF THE BYLAWS
         IS HEREBY DELETED AND THE WORD "RESERVED " IS HEREBY SUBSTITUTED IN ITS
         PLACE.

This Amendment is effective as of January 5, 1996.