A set of reconstruction includes an element of reconstruction (1) having a base part (11) and an upper part (10) connected to the base part (11) or intended to be connected to this base part (11) the base part (11) includes elements (12, 25, 26) for its mounting on the external side of the humeral implant (2) it is sized to project, after installation on the humeral implant (2), beyond the external surface (2a) of the humeral implant (2) and beyond at least one of the anterior (2b) or posterior (2c) surfaces of this humeral implant (2), on the outer side of these surfaces and the upper part (10) forms an outer external curved surface extending, after mounting on the humeral implant (2), away from the external surface (2a) of this humeral implant (2) and from at least one of the anterior or posterior surfaces of this humeral implant.
