In municipalities of less than 500,000 population, where a variation is to be made by ordinance, upon the report of the board of appeals, the corporate authorities, by ordinance, without further public hearing, may adopt any proposed variation or may refer it back to the board for further consideration, and any proposed variation which fails to receive the approval of the board of appeals shall not be passed except by the favorable vote of two-thirds of all alderpersons or trustees of the municipality.
65 ILCS 5/11-13-10