  By analogy to the continuous Painlev\'e II equation, we present particular
solutions of the discrete Painlev\'e II (d-P$\rm_{II}$) equation. These
solutions are of rational and special function (Airy) type. Our analysis is
based on the bilinear formalism that allows us to obtain the $\tau$ function
for d-P$\rm_{II}$. Two different forms of bilinear d-P$\rm_{II}$ are obtained
and we show that they can be related by a simple gauge transformation.
