It means more uncertainty for four secondaries in East Kilbride and three in Hamilton.
The council, which met on Wednesday and approved other plans for a pound;182 million public private partnership (PPP) programme, pledged to put new proposals out for statutory consultation before the start of the summer break.
It had always insisted its plans were not "a done deal". While they had led to casualties among councillors in the recent local government elections, Eddie McAvoy, the council leader, pointed out that parents at 18 of 21 secondaries had backed the proposals in a consultation which lasted 82 days.
The approval rating was 72 per cent - but only 11 per cent of parents voted.