The four voted with the Scottish National Party in a row over the council's handling of a reorganisation of its management system and a resulting employment tribunal.
Deputy chief executive Ian Leitch took the council to tribunal because he was sacked as a result of reorganisation, and was awarded£50,000 compensation.
The four rebels were disciplined by the Labour Party and left to form their own group - the Independent Community Representatives.
The council now has no leader or deputy; a meeting was expected this week to decide its future.
Referring to the meeting, renegade councillor Danny McCafferty said: 'There will be motions and counter motions and deals will be done as people try to take control.'
The move resulted in Mr McCafferty being sacked as education and children's services spokesperson for the Convention of Scottish Local Authorities because he is no longer a member of the Labour group.
A spokesman for the Labour group at the council criticised one of the breakaway members, John Syme, who he said was on sick leave from Glasgow City Council where he is employed as a housing officer.
Mr Syme said: 'I do not work for Glasgow in the evenings and the meeting is being held at 7pm. I have not claimed from [Glasgow] since I have been off sick.'