The application is concerned with a cover of an airbag unit in a motor vehicle which is equipped with a tear-open line and has a foam-backed foil and the process for making the cover. The process includes:a) heating a foil in the region of the intended tear-open line;b) forming a channel in the foil which is drawn-in in relation to the adjoining face of the foil in the region of the tear-open line;c) creating a reduction in wall thickness of the foil at the tear-open line, located at a channel bottom, by high-frequency embossing;d) introducing the foil into a mold and foam backing the foil;e) producing a smaller wall thickness in the foam backing in the region of the tear-open line.