Cutting tool has a substrate and a multilayer coating deposited by PVD. The coating comprises a base layer of one or more identical or different layers of a nitride or carbonitride which contains at least aluminium (Al) and a chromium-containing, oxidic functional layer. Attachment of the chromium-containing functional layer is improved by an intermediate layer of one or more oxides or oxide nitrates of the metals Al, Cr, Si, and/or Zr provided between the base layer and the functional layer. The intermediate layer has a cubic structure and the chromium-containing functional layer is selected from chromium oxide (Cr2O3), chromium oxynitride, aluminium-chromium oxide (AlCr)2O3, aluminium-chromium oxynitride or a mixed oxide or mixed oxynitride of aluminium, chromium and further metals of (AlCrMe1, Men)2 oxide or (AlCrMe1, Men)2 oxynitride, where Me . . . Men means one or more further metals, selected from Hf, Y, Zr and Ru, and wherein the functional layer has a rhombohedral structure.