Abstract: A method for producing a tubular-shaped wire mesh which serves as cladding for catalytically coated cylindrical one-piece ceramics units used to decontaminate exhausts of internal combustion engines. These units function as catalysts and have a wire mesh wrapped along a circumference and around the surface of an arbor of the unit. The wrapping is such that the mesh is axially longer than the distance between two end faces of the units. The mesh has a section projecting axially beyond each end face of the unit. The wire mesh is secured to the surface of the arbor in an area which is directly adjacent to the projecting section. The projecting section is compressed into a bead to a predetermined axial extent.