Claire Bridgman, who represents Drum Brae / Gyle ward, will now sit as an independent.
Her resignation follows those of former planning convener Lewis Ritchie in February and former housing and economy convener Gavin Barrie in April.
It leaves the Tories - who were hit by a resignation of their own earlier this month when Ashley Graczyk quit the group - as the largest party on the council with 17 seats to the SNP’s 16.
Cllr Bridgman’s resignation is not likely to threaten the continuation of SNP-Labour rule at the City Chambers.
But opposition parties were quick to claim the administration was now in “absolute chaos” and the SNP group was “falling apart”.