A glenoid implant for an inverted shoulder prosthesis, comprising: - a base intended to be anchored on a glenoid cavity of a scapula and having a main orifice crossing the base; - a glenosphere defining a convex articulation surface formed in a spherical portion and having a central orifice crossing the glenosphere, wherein said glenosphere is mounted on said base by mutual wedging between female and male conical bearing surfaces (33, 42) provided on the glenosphere and on the base; - a main anchoring screw crossing the main orifice of said base and shaped for anchorage of the base on the glenoid cavity, wherein said main anchoring screw comprises a main head and an anchor rod having an end segment provided with an external tapping; - a locking screw, coaxial with the main anchoring screw, crossing the central orifice of the glenosphere to lock the glenosphere on the base in a locked position, wherein said locking screw comprises a proximal head and a locking rod having an intermediate segment provided with an external tapping and extended by an end segment; wherein: - the main anchoring screw has an inner hole opening into the main head and having successively, starting from the main head and in the direction of the end segment of the anchor rod, an inlet portion shaped so as to cooperate with a screwing tool, an intermediate portion provided with a threading and a tip portion; - the locking rod has its end segment which has a length longer than a cumulated length of the inlet portion and of the intermediate portion of the inner hole of the main anchoring screw, so that said end segment of the locking rod is intended to slide inside the tip portion of the inner hole of the main anchoring screw to center the female and male conical bearing surfaces (33, 42) relative to one another, and the intermediate segment of the locking rod is intended to cooperate afterwards by screwing with the intermediate portion of the inner hole of the main anchoring screw to lock the mutual wedging of the female and male conical bearing surfaces (33, 42), the proximal head of the locking screw abutting on an annular bearing surface provided inside the central orifice of the glenosphere, and wherein the central orifice of the glenosphere has successively, starting from the convex articulation surface in the direction of the base, a proximal portion shaped so as to completely receive the proximal head of the locking screw, and a distal portion provided with a threading complementary to the external tapping of the intermediate segment of the locking rod of the locking screw, wherein the annular bearing surface of the central orifice of the glenosphere is provided at the interface between said proximal portion and said distal portion. - a base intended to be anchored on a glenoid cavity of a scapula and having a main orifice crossing the base; - a glenosphere defining a convex articulation surface formed in a spherical portion and having a central orifice crossing the glenosphere, wherein said glenosphere is mounted on said base by mutual wedging between female and male conical bearing surfaces (33, 42) provided on the glenosphere and on the base; - a main anchoring screw crossing the main orifice of said base and shaped for anchorage of the base on the glenoid cavity, wherein said main anchoring screw comprises a main head and an anchor rod having an end segment provided with an external tapping; - a locking screw, coaxial with the main anchoring screw, crossing the central orifice of the glenosphere to lock the glenosphere on the base in a locked position, wherein said locking screw comprises a proximal head and a locking rod having an intermediate segment provided with an external tapping and extended by an end segment; - the main anchoring screw has an inner hole opening into the main head and having successively, starting from the main head and in the direction of the end segment of the anchor rod, an inlet portion shaped so as to cooperate with a screwing tool, an intermediate portion provided with a threading and a tip portion; - the locking rod has its end segment which has a length longer than a cumulated length of the inlet portion and of the intermediate portion of the inner hole of the main anchoring screw, so that said end segment of the locking rod is intended to slide inside the tip portion of the inner hole of the main anchoring screw to center the female and male conical bearing surfaces (33, 42) relative to one another, and the intermediate segment of the locking rod is intended to cooperate afterwards by screwing with the intermediate portion of the inner hole of the main anchoring screw to lock the mutual wedging of the female and male conical bearing surfaces (33, 42), the proximal head of the locking screw abutting on an annular bearing surface provided inside the central orifice of the glenosphere,