A metal reinforcing piece for mounting on a leading edge or trailing edge of a composite blade for a turbine engine is made by shaping two metal sheets, positioning them on either side of a core, assembling the two sheets together around the core under a vacuum, shaping them on the core by hot isostatic compression, and cutting them to separate the reinforcing piece and release the core. A predetermined roughness is given to at least a portion of the surface of the core and is transferred to a corresponding portion of an inside surface of the reinforcing piece by the hot isostatic compression.