The glenohumeral component of the invention comprises a first side and a second side, which are opposite each other and which, in an implanted state in which the glenohumeral component is free-floating with respect to a humerus and a glenoid of a human shoulder, are in contact respectively with an end portion of the humerus and with a glenoid component intended to be secured to the glenoid. The first side of the glenohumeral component includes a convex articular surface that is designed to articulate with a concave bone surface prepared within the end portion of the humerus. The second side of the glenohumeral component includes a concave articular surface that is designed to articulate with a convex articular surface of the glenoid component. The corresponding shoulder prosthesis is thus reversed. Moreover, the articular interface between the glenoid component, which is secured to the glenoid, and the rest of the prosthesis has double mobility, which provides a greater range of motion between the glenoid and the humerus.