  We study discrete conjugate nets whose Laplace sequence is of period four.
Corresponding points of opposite nets in this cyclic sequence have equal
osculating planes in different net directions, that is, they correspond in an
asymptotic transformation. We show that this implies that the connecting lines
of corresponding points form a discrete W-congruence. We derive some properties
of discrete Laplace cycles of period four and describe two explicit methods for
their construction.
