The proposed resolution was created by the city attorney after Mayor Jenifer Bingham had tried to replace the police chief and the city clerk last month.
If approved, the new rule would change the way appointments are made.
It would require a single council member to be designated as chairman of a committee.
Each chairman would oversee a specific department within the city such as police, cable, water and sewer.
That person would also be in charge of any changes made within the department instead of the mayor deciding.
Each chairman would be elected by a majority vote of the council starting next week..
Attorney to 6 council members Kevin Cure says,
"The resolution stands a good chance of passing...we'll have some more legislation for them to consider next Tuesday night that will restore some reasonableness, and authority to the 6 council members who want to execute what they've been elected to do."
The city council will meet again next Tuesday May 8th to appoint members to each committee.
They will also discuss the police chief's future.