Abstract: The tool face 12 and the flank 13 as well as the cutting edge 14 of a carbide cutting tip 19 for the fine machining of bores or the like are coated with a thin hard-material coating 21, 22 of TiC or TiCN by the PVD method and this coating is not partly ground off again subsequently, as practiced in cutting tips coated by the CVD method to restore a shaper cutting edge. As a result of the fully retained coating, inter alia both the flank wear is reduced and the chip flow over the toll face is improved, which produces an excellent surface quality of a bore. The cutting tip is especially suitable for single-blade reamers.