The component has a metallic unit (22) defining a convex articulation surface (S 2) which has a semi-sphere shape and centered on a symmetry axis (X 2 - X` 2). The symmetry axis is not perpendicular to rear side (26) of the component. The symmetry axis is directed towards base (21), when the rear side of the component is vertical. The component is configured such that the symmetry axis is horizontal when a patient stands. An independent claim is also included for an overall shoulder prosthesis including a glenoidal component.
