There is now provided a body of cemented carbide, Si3N4 or another ceramic material, coated by at least one CVD or PVD diamond or cBN layer with a chromium nitride, chromium carbide or chromium carbonitride layer. The chromium-containing layer is outside the diamond layer which in the case of more than one diamond layer is the outermost diamond layer of the coating. Improved machining properties are obtained.