North Lanarkshire took the decision to remain in Cosla at its full council meeting yesterday.
An eighth Labour council, West Dunbartonshire, confirmed it planned to leave the umbrella group at a special meeting earlier this week and will give the organisation 12 month's notice of its intention to quit.
Several other large Labour-run councils, many in the west of Scotland, also intend to leave.
One of West Dunbartonshire's concerns was that it could have to stump up a higher share of Cosla's costs in the future if it has fewer members. The issue over Cosla membership for many councils centres on a dispute over where power should lie within the organisation.