CHICAGO — A group that advises a small portion of McDonald’s shareholders says the company’s board needs a makeover as much as the menu.

CtW Investment Group, which works with a number of union pension funds, laid out its demands in a letter sent Friday to the board. The letter comes about two weeks after McDonald’s, based in the Chicago suburb of Oak Brook, named Steve Easterbrook to replace Don Thompson as CEO as the burger giant struggles.

“Returning McDonald’s Corp. to a path of long-term, profitable growth requires that Mr. Steven Easterbrook’s appointment as CEO is followed by a robust refreshment of the board’s membership and leadership,” CtW Executive Director Dieter Waizenegger wrote in the letter, a copy of which was reviewed by the Chicago Tribune.

The letter, addressed to Chairman Andrew McKenna and board member Miles White, chairman of the board’s governance committee, was sent to the full board, CtW said.

On Jan. 28, the same day Easterbrook’s appointment was announced, McDonald’s also added Google executive Margo Georgiadis to its board. Easterbrook is set to join the board when he becomes CEO in March.

Waizenegger said recruiting Georgiadis was “a positive step” but asked that the company do more to refresh its board. He wants to see McDonald’s come up with and publicly disclose plans to change the board’s leadership, including having a board succession plan. He also said CtW believes it is the right time to “transition board leadership.”

The board, with many long-tenured directors “overwhelmingly drawn from local Chicago-networks,” needs to “critically review its performance and culpability,” Waizenegger wrote.

CtW would like to see the board use a broader approach when it comes to finding new members.

In a statement Friday evening, McDonald’s praised its board of directors.