A multilayer adhesive tape having a backing based on an oriented thermoplastic film, whose upper face is coated, if desired, with a release coating and to whose lower face the following layers have been applied: a) a primer layer which is not applied over the full area and which anchors very well to the thermoplastic film, b) a release layer which is applied over the full area of the applied primer layer, and the free thermoplastic film surface, the release layer anchoring better to the primer layer than to the thermoplastic film, c) a pressure-sensitive adhesive composition which is applied over the full area of the release layer and which is anchored better on the release layer than the release layer on the thermoplastic film, d) the release layer consisting of an acrylate copolymer dispersion and at least one further component.