Exhibit 4.2

DESCRIPTION OF EQUITY SECURITIES REGISTERED
UNDER SECTION 12 OF THE EXCHANGE ACT

Randolph Bancorp, Inc. (the “Company”) has one class of securities registered under Section 12 of the Securities Exchange Act of 1934, as amended: common stock, par value $0.01 per share (the “Common Stock”). The Company’s Common Stock is traded on the NASDAQ Global Select Market under the symbol “RNDB.”

The following is a description of the material terms and provisions of the Company’s Common Stock. It may not contain all the information that is important to you. Therefore, you should read the Company’s articles of organization and bylaws, which are attached as exhibits to the Annual Report on Form 10-K to which this description is an exhibit.

General

Under the Company’s articles of organization the Company has authority, without further shareholder action, to issue 15,000,000 shares of Common Stock. The Company may amend its articles of organization from time to time to increase the number of authorized shares of Common Stock. Any such amendment would require the approval of the holders of a majority of the Company’s Common Stock entitled to vote. Amendments to the articles of organization require a two-thirds shareholder vote in certain circumstances.

Dividends

The Company can pay dividends on its Common Stock if, after giving effect to the distribution, it would be able to pay its indebtedness as the indebtedness comes due in the usual course of business and its total assets exceed the sum of its liabilities and the amount needed, if the Company were to be dissolved at the time of the distribution, to satisfy the preferential rights upon dissolution of any holders of capital stock who have a preference in the event of dissolution. The holders of Common Stock will be entitled to receive and share equally in dividends as may be declared by the Company’s board of directors out of funds legally available therefor.

Voting Rights

The holders of the Company’s Common Stock have exclusive voting rights, including the election of the board of directors, and to act on all other matters as are required to be presented to them under Massachusetts law or as are otherwise presented to them by the board of directors. Generally, each holder of Common Stock is entitled to one vote per share and will not have any right to cumulate votes in the election of directors. Any person who beneficially owns more than 10% of the then-outstanding shares of the Company’s Common Stock, however, will not be entitled or permitted to vote any shares of Common Stock held in excess of the 10% limit during the three-year period following the offering and conversion; thereafter, shares of Common Stock in excess of the 10% limit will be entitled to cast 1/100^th of a vote per share.

Liquidation

In the event of any liquidation, dissolution or winding up of the Company, the holders of its Common Stock would be entitled to receive, after payment or provision for payment of all its debts and liabilities, all of the assets of the Company available for distribution, and eligible account holders and supplemental eligible account holders will be treated as surrendering their rights to the Company’s liquidation account.

Preemptive Rights

Holders of the Company’s Common Stock do not have preemptive rights with respect to any shares, unless such preemptive rights are approved by the board of directors. The Company’s Common Stock cannot be redeemed.