The invention relates to a prosthesis for implantation into a living body in the form of a magnetic artificial joint, in particular an artificial shoulder joint, comprising:a) a first prosthesis member comprising a socket member,b) a second prosthesis member comprising a head member,c) one of the socket member and the head member is at least partially composed as a permanent magnet and the other one of the socket member and the head member is at least partially composed of a magnetic material, or the socket member and the head member are both at least partially composed as a permanent magnet,d) the socket member comprises a recess on a surface side to be coupled with the head member, the recess comprising a concavely contoured contact surface,e) the head member comprises a projection on a surface side to be coupled with the socket member, the projection comprising a convexly contoured contact surface,f) the convexly contoured contact surface is adapted to the concavely contoured contact surface, such that the head member can be coupled in a rotatably jointed manner to the socket member in the nature of a ball/ball-socket joint,g) wherein the convexly contoured contact surface can perform a generally slip-fee rolling motion or a combined slipping and rolling motion on the concavely contoured contact surface in reaction to a change of an angle between the first and the second prosthesis member, and the convexly contoured contact surface can be shifted across the concavely contoured contact surface within a shifting area.