The male and female parts of a hip prosthesis each comprise two parts, a base fixed to the bone, and an active organ attached removably to the base. The upper face of the base has a truncated conical bore with a threaded bore at the bottom. The active member has a conically shaped projection with a threaded end which matches the bore in the base and which is screwed in the base to effectively lock the active member to the base. Diametrically opposite flat parts on the base and active member are provided to allow the active member to rotate while preventing the base from rotating.