The invention pertains to a processing insert comprised of a body with a hard metal or ceramic substrate and with a multilayer coating and the manufacture of same. In order to have a highly fracture-tough insert with a relatively thick coating, it is suggested that an external layer (protective layer) be applied according to the CVD process, said layer being either a monophase or multiphase layer of Zr-based or Hf-based carbide nitride or carbonitride, and presenting internal compressive stresses. The layer(s) underlying the external layer, also applied according to the CVD process, also present(s), without any exception, internal compressive stresses, while at least one of them, maybe the only one laying under the protective layer is made of TiN, TiC and/or TiCN. The coating is applied according to a continuous CVD process at temperatures of 900° C. to 1100° C. and involves a specific modification of the gas compounds.