  We apply the supersymmetric procedure to one-step random walks in one
dimension at the level of the usual master equation, extending a study
initiated by H.R. Jauslin [Phys. Rev. A {\bf 41}, 3407 (1990)]. A discussion of
the supersymmetric technique for this discrete case is presented by introducing
a formal second-order discrete master derivative and its ``square root", and we
solve completely, and in matrix form, the cases of homogeneous random walks
(constant jumping rates). A simple generalization of Jauslin's results to two
uncorrelated axes is also provided. There may be many applications, especially
to bistable and multistable one-step processes.
