This glenoidal component for a shoulder prosthesis comprises a base which may be immobilized on the glenoid cavity of a shoulder, and an element provided to be mounted on this base and forming a convex surface of articulation centered on an axis of symmetry. This axis of symmetry is non perpendicular to a rear face of the base intended to abut against the glenoid cavity, this making it possible to compensate a defect in parallelism between the resectioned surface of the glenoid cavity and the axis of the patient's spinal column.A surgeon can select the component most adapted to the orientation of the resectioned surface from a set of components in which the axes of symmetry of the components are oriented differently with respect to their rear faces.
