The invention provides a method of making a piece of metal reinforcement for mounting on the leading or trailing edge of a composite turbine engine blade, the method comprising the steps consisting in positioning two metal sheets (1) on either side of a core (2), in shaping the sheets (1) on the core (2) by hot isostatic compression, and in cutting the sheets (1) in order to separate the reinforcement along at least one line of cut and in order to release the core. The core (2) has projecting sacrificial zones (13), with the sheets (1) being cut along the sacrificial zones (13) without degrading the remainder of the core (2).