Inverse prosthesis of the shoulder for the articulation of a humerus in a scapula of a shoulder comprising a glenoid cavity. The prosthesis includes an at least partly convex articulation element, including elements for support and attachment to the glenoid cavity, and able to articulate with an at least partly concave mating articulation element, associated with the top of the humerus. The articulation element includes a substantially hemi-spherical element and a pin-type implant element made as distinct and reciprocally removable elements, so as to allow them to be assembled sequentially with respect to the glenoid cavity.