A cotyloid implant for a hip prosthesis, includes a first type of insert (2) with a spherical internal cavity (2a), for the mounting of a hemispherical core (4) with a capacity for mobility which has an internal cavity (4a) for co-operation with articulation with a femoral head, a second type of insert with an internal cavity for cooperation with a femoral head with articulation, characterised in that the centre of rotation of the femoral head is different from the axis of rotation of the first type of insert (2) and/or of the second type of insert.