A composite film for closing a container by sealing the composite film against a circumferential sealing surface of the container or of a cap ring to be connected to the container has a support layer made of a metal film and a sealing layer connected to the metal film. The sealing layer comprises a coextruded layer with a cohesively breaking intermediate layer and adhesion promoter layers arranged on both sides of the intermediate layer. The composite film is suitable for tight sealing against sealing surfaces made of polished tinplate.