Permanent magnets or electromagnets or a combination of such magnets are provided to retain a prosthetic device on an extremity or limb, such as an amputated arm. The prosthesis utilizes the opposing forces, which are developed by virtue of like magnetic poles being in proximity to each other, to urge the prosthesis to remain attached to the extremity. The prosthesis is prevented from rotation by virtue of a centering force that is provided by an attachment magnet in the prosthesis being placed between two implanted magnets. A removable mounting ring is placed over the prosthesis to maintain it on the extremity.