A glenoid component (2) of a shoulder joint prosthesis for fixation to the glenoidregion of a scapula, comprises a body part (16) of the prosthesis which presentsa surface for articulation with the corresponding articulating surface of ahumeral component, and a frame part (4). The frame part has a lateral surface (20)on which the body part can be mounted, and a medial surface (22) generally oppositethe lateral surface. First and second bores (24,26) extend between the lateraland medial surfaces for receiving screws (16, 18) so as to fasten the frame partto the scapula. The bores are configured so that their axes (28, 30) converge,so that the distance measured between the axes decreases with increasing distanceaway from the medial surface of the frame towards the scapula.