A support sleeve made of a metallic material, preferably of nickel, is provided at at least one longitudinal end with a chamfer running all around in the inner circumference. This prevents damage to a film-like coating or thin intermediate sleeve, which surrounds the cylinder core to which the sleeve is fitted. A device for chamfering and deburring the longitudinal ends of the sleeve include a supporting body having a cylindrical journal with a diameter only slightly smaller than the internal diameter of the sleeve to be machined, in order to accommodate a longitudinal end of the sleeve and to guide the cut. A cutting holder is machined on the supporting body by means of which holder a cutter can be brought up to the inner circumference of the longitudinal end of the sleeve to be machined, and the supporting body can be rotated relative to the sleeve to be machined and pushed onto the journal.