Councillor David Macdonald was one of two independents who helped Labour form a minority administration in late May but he has now resigned.
His decision, which also includes giving up his role as convener for health and social care, means the administration is formed of six councillors — the same number as the SNP returned at the election.
Councillor Katie Pragnell from Labour has been voted in as the new health convener.
Councillor Macdonald, who represents Clarkston, Netherlee and Williamwood, said he would not be commenting on his resignation.
However, responding to a query on social media, he said: “The agreement I reached with the Labour group leader for my support to install a minority Labour, Independent administration was not going to be delivered.
“I lost trust and confidence and for that reason I could not, in good faith, continue.”
Council leader Owen O’Donnell, the Labour group boss, said his administration, which includes independent Councillor Danny Devlin, would aim to “build consensus” vote by vote.
He said: “We can confirm that Councillor Macdonald has resigned from the administration.
“The Labour minority administration including Danny Devlin remains committed to delivering its manifesto and in particular in response to the cost of living crisis.
“We will continue to try and build consensus across all parties, including Councillor Macdonald, on a vote by vote basis.”
Before May’s election, the SNP, Labour and Councillor Devlin had worked in coalition in East Renfrewshire for a decade. However, Scottish Labour leader Anas Sarwar pledged his party would not enter coalitions with the SNP or Conservatives.
The five Conservative councillors backed all Labour’s nominations for key roles at the first meeting of the new term in late May, with the SNP group claiming a “backroom deal” had been reached.
It accused Labour of “getting into bed” with the Tories.
Labour members abstained as Conservatives, with the backing of the two independents were appointed deputy provost, chair of the audit and scrutiny committee and chair of the licensing committee.