A replacement joint for a human body and a method of installing such a replacement joint is provided. A ball portion of the replacement joint is installed on an end of a first bone. A receptacle having an engagement surface that has an aspherical configuration is formed in a second bone. A socket portion of the replacement joint is inserted in the receptacle so as to receive the ball portion on the first bone. The socket portion has an engagement surface with an aspherical configuration complementary to the engagement surface of the receptacle in the second bone. The configurations of the engagement surfaces of the socket portion and the receptacle in the second bone are such that inserting the socket portion in the receptacle in the second bone provides the socket portion with at least four degrees of constraint.