Aberdeen City Council is giving a year's notice to quit, following a similar move by Dumfries and Galloway Council last month.
Aberdeen finance convener Willie Young said: "We are finding now that Cosla has lost its teeth. That is thanks primarily to the Scottish Government, who are no longer negotiating with Cosla but are imposing things onto Cosla such as the rural schools decisions.
"We hope that by coming out of Cosla and starting to negotiate with the Scottish Government directly, Aberdeen will get its fair share."
A Cosla spokesman said: "This is not a surprise. Cosla as a membership organisation is governed by a set of rules. This notice to quit is a member council following our procedures, which in itself is a good thing. The reason for it happening now is that under our rules a council has to give a full financial year's notice. Indeed this is why you could see more councils deciding to take a similar course of action."