A method of making a metal reinforcing member that is to be mounted on a leading edge or a trailing edge of a composite blade of a turbine engine, the method including: shaping two metal sheets, positioning them on either side of a core including at least one recess that is to form a mold for a spacer for positioning the reinforcing member, assembling them together under a vacuum, conforming them against the core by hot isostatic compression, and cutting them to separate the reinforcing member and release the core.