The present invention cemented carbide (cemented carbide), cermet, steel or a substrate of high speed steel (HSS), and, by the PVD process relates to a cutting tool having a multilayer coating deposited on a substrate, the multilayer coating comprises at least aluminum (Al) and, optionally, Al, Cr, Si, Y, Ru and containing additional metal or more selected from Mo, a base of the same or different layers, at least one of a nitride or carbonitride which is disposed on the other one of the upper a layer, and a chromium-containing oxide (oxidic) the functional layer. In order to improve the adhesion of the chromium-containing functional layer, in accordance with the present invention, a metal of Al, Cr, Si, and / or Zr at least one intermediate layer of oxide, or oxide nitrate is provided between the base layer and the functional layer, the intermediate layer has a cubic crystal structure, the chromium-containing functional layer of chromium oxide (Cr ₂ O _3), chromium oxynitride, aluminum-chromium oxide _{((AlCr) 2 O 3)} , aluminum-chromium oxynitride, or aluminum, chromium and a mixed oxide of the additional metal _{((AlCrMe 1, Me n)} 2 -oxide) is selected from or mixed oxynitride _{((AlCrMe 1, Me n)} 2 oxynitride), wherein Me, Me ... _n is Hf, Y, means that at least one further metal selected from Zr, and Ru, and the functional layer and has a trigonal (rhomohedral) structure.