A semiconductor substrate (1) is provided with integrated circuits. Dicing trenches (7) are formed in the substrate (1) between the integrated circuits, a polyimide layer (8) spanning the trenches (7) is applied above the integrated circuits, a tape layer (14) is applied above the polyimide layer (8), and a layer portion of the substrate (1) is removed from the substrate side (17) opposite the tape layer (14), until the trenches (7) are opened and dicing of the substrate (1) is thus effected. The polyimide layer (8) is severed in sections (18) above the trenches (7) when the tape layer (14) is removed. The semiconductor chip is provided with a cover layer (11) laterally confining the polyimide layer (8) near the trenches (7), in particular for forming breaking delimitations (9).