A cooking system includes a cooking appliance with a microwave heat source and a cooking container for receiving food. The cooking appliance includes a cooking chamber having a muffle and a support device arranged on the muffle that positions the cooking container in the cooking chamber. The cooking container has a base and four side walls arranged transversely to the base as two opposing longitudinal sides and two opposing broadsides. The cooking container, at transitions from the two opposing broadsides to the two opposing longitudinal sides, has four corners, each of which has a rounded region having an external radius of at least 30 mm to maintain a minimum spacing from the muffle to counteract electrical flashovers between the cooking container and the cooking chamber.