The discrete dynamical system of absolute differences defined by the map [psi]( x[subscript 1] , x[subscript 2] , x[subscript 3] , x[subscript 4] ) = ([vertical line] x[subscript 2] - x[subscript 1] [vertical line], [vertical line] x[subscript 3] - x[subscript 2] [vertical line], [vertical line] x[subscript 4] - x[subscript 3] [vertical line], [vertical line] x[subscript 1] - x[subscript 4] [vertical line]) has been studied by many authors and one of the interesting questions is how to locate quadruples which converge to the fixed point (0, 0, 0, 0) in large numbers of steps. An elementary method is offered for obtaining such quadruples. The method is also able to find quadruples that will not converge to (0, 0, 0, 0). (Contains 2 tables.)