The present invention provides a new and improved method and apparatus for reconstructing a joint. More particularly, the present invention provides a new and improved joint prothesis comprising a stem, a neck angled off the stem, and a head set at the end of the neck, wherein the stem, neck and head utilize new and improved connection mechanisms for providing a greater range of assembly configurations. Among other things, the present invention provides a new and improved joint prosthesis which permits adjustment of the longitudinal extension, lateral offset and angle of inclination of the head relative to the cut surface of the humerus. In one preferred form of the invention, there is provided a joint prosthesis assembly comprising: a stem having a proximal end and a distal end and a longitudinal axis extending therebetween; a neck extending from the proximal end of the stem at an angle to the longitudinal axis of the stem, wherein the neck comprises a proximal end and a distal end and a longitudinal axis extending therebetween, and wherein the neck further comprises a first rounded end surface and a second non-circular end surface; a trunnion for mounting the neck to the stem, wherein the trunnion comprises a recess comprising a first rounded inner surface and a second non-circular inner surface wherein: the recess is configured to selectively and snugly receive the neck therein, such that when the neck is received by the recess, the trunnion is held in a non-rotational relationship with respect to the neck's longitudinal axis while permitting rotation about the other two axes.