Rep. Jim Jordan (left), now the House Judiciary Committee chairman and the longtime Republican stalwart, has emerged as a top contender to replace former House Speaker Kevin McCarthy (right).

Saying they are “ashamed and embarrassed” by the ouster of Speaker Kevin McCarthy, four California GOP lawmakers joined 41 other House Republicans to strongly urge changes in how a speaker is selected and retained.

“The injustice we all witnessed cannot go unaddressed — lest we bear responsibility for the consequences that follow. Our Conference must address fundamental changes to the structure of our majority to ensure success for the American people,” the letter to House Republican colleagues said.

Among those signing were Reps. David Valadao, Ken Calvert, John Duarte and Young Kim.

McCarthy became the first speaker in history Tuesday to lose his job because of a vote by his colleagues. It was set in motion by a newly adopted rule allowing one lawmaker to demand such a vote, known as a “motion to vacate.”

In January, McCarthy agreed to the one-member rule as a way of placating far-right lawmakers, many of whom had long questioned his support for their causes.

In their letter, the 45 Republicans noted that McCarthy lost his speakership with less than 4% of the Republican caucus. Eight Republicans joined 208 Democrats to topple the Bakersfield Republican. All 11 California Republican House members voted to retain McCarthy.

“We cannot allow our majority to be dictated to by the alliance between the chaos caucus and theminority party that will do nothing more than guarantee the failure of our next Speaker.,”’ the letter said.

The letter was signed mostly by center-right Republicans, though it included two committee chairmen . House Ways and Means Committee Chairman Jason Smith, R-Mo. and Foreign Affairs Committee Chairman Michael McCaul, R-Texas.

The letter urging changes in the rules could be crucial as Republicans struggle to choose a successor. The party’s caucus plans to hold a candidate forum Tuesday and a party vote Wednesday. If a candidate is chosen, it would then go to the full House.

There’s no timetable, and no one appears close at this point to winning the 218 votes needed to become speaker.