Exhibit 4.2

DESCRIPTION OF WILLIAM PENN BANCORPORATION’S COMMON STOCK

REGISTERED UNDER SECTION 12 OF THE SECURITIES EXCHANGE ACT OF 1934

William Penn Bancorporation is incorporated in the State of Maryland. The rights of our shareholders are generally covered by Maryland law and our articles of incorporation and bylaws (each as amended and in effect on the date hereof). The terms of our common stock are therefore subject to Maryland law, including the Maryland General Corporation Law, and the common and constitutional law of Maryland.

This exhibit describes the general terms of our common stock. This is a summary and does not purport to be complete. Our articles of incorporation and bylaws as they exist on the date of this Annual Report on Form 10-K are incorporated by reference or filed as an exhibit to the Annual Report on Form 10-K of which this exhibit is a part, and amendments or restatements of each will be filed with the Securities and Exchange Commission (the “SEC”) in future periodic or current reports in accordance with the rules of the SEC. You are encouraged to read these documents.

For more detailed information about the rights of our common stock, you should refer to our articles of incorporation and bylaws and the applicable provisions of Maryland law, including the Maryland General Corporation Law, for additional information.

General

William Penn Bancorporation is authorized to issue 150,000,000 shares of common stock having a par value of $0.01 per share and 50,000,000 shares of preferred stock having a par value of $0.01 per share. Each share of William Penn Bancorporation’s common stock has the same relative rights as, and is identical in all respects with, each other share of common stock. Upon payment of the purchase price for the common stock, as required by the plan of conversion, all stock will be duly authorized, fully paid and nonassessable. William Penn Bancorporation will not issue any shares of preferred stock in the conversion and offering.

Dividends

William Penn Bancorporation can pay dividends if, as and when declared by its board of directors. The payment of dividends by William Penn Bancorporation is limited by law and applicable regulation. See “Our Dividend Policy.” The holders of common stock of William Penn Bancorporation will be entitled to receive and share equally in dividends declared by the board of directors of William Penn Bancorporation. If William Penn Bancorporation issues preferred stock, the holders of the preferred stock may have a priority over the holders of the common stock with respect to dividends.

Voting Rights

The holders of common stock of William Penn Bancorporation will possess exclusive voting rights in William Penn Bancorporation. They will elect William Penn Bancorporation’s board of directors and act on other matters as are required to be presented to them under Maryland law or as are otherwise presented to them by the board of directors. Except as discussed in “Restrictions on Acquisition of William Penn Bancorporation,” each holder of common stock will be entitled to one vote per share and will not have any right to cumulate votes in the election of directors. If William Penn Bancorporation issues preferred stock, holders of William Penn Bancorporation preferred stock may also possess voting rights.

Liquidation

If there is any liquidation, dissolution or winding up of William Penn Bank, William Penn Bancorporation, as the sole holder of William Penn Bank’s capital stock, would be entitled to receive all of William Penn Bank’s assets available for distribution after payment or provision for payment of all debts and liabilities of William Penn Bank, including all deposit accounts and accrued interest. Upon liquidation, dissolution or winding up of William Penn Bancorporation, the holders of its common stock would be entitled to receive all of the assets of William Penn

Bancorporation available for distribution after payment or provision for payment of all its debts and liabilities. If William Penn Bancorporation issues preferred stock, the preferred stock holders may have a priority over the holders of the common stock upon liquidation or dissolution.

Preemptive Rights; Redemption

Holders of the common stock of William Penn Bancorporation will not be entitled to preemptive rights with respect to any shares that may be issued. The common stock cannot be redeemed.

Exclusive Forum for Certain Stockholder Litigation Matters

The bylaws of William Penn Bancorporation provide that, unless William Penn Bancorporation consents in writing to the selection of an alternative forum, the sole and exclusive forum for (i) any derivative action or proceeding brought on behalf of William Penn Bancorporation, (ii) any action asserting a claim of breach of a fiduciary duty owed to William Penn Bancorporation or William Penn Bancorporation’s stockholders by any director, officer or other employee of William Penn Bancorporation, (iii) any action asserting a claim arising pursuant to any provision of the Maryland General Corporation Law, or (iv) any action asserting a claim governed by the internal affairs doctrine shall be a state or federal court located within the State of Maryland. This exclusive forum provision does not apply to claims arising under the federal securities laws.