  We first obtain by analogy with the continuous (differential) case the
general solution of a discrete Riccati equation. Our results can be considered
the discrete analog of Mielnik's construction in supersymmetric quantum
mechanics [J. Math. Phys. 25, 3387 (1984)]. Moreover, we establish the full
equivalence between our discrete Riccati equation and a corresponding
homogeneous second order discrete linear equation. We present an application to
the three-site master equation obtaining explicitly the general solutions for
the simple cases of free random walk and the biased random walk
