  We present a systematic approach to the construction of Miura transformations
for discrete Painlev\'e equations. Our method is based on the bilinear
formalism and we start with the expression of the nonlinear discrete equation
in terms of $\tau$-functions. Elimination of $\tau$-functions from the
resulting system leads to another nonlinear equation, which is a ``modified''
version of the original equation. The procedure therefore yields Miura
transformations. In this letter, we illustrate this approach by reproducing
previously known Miura transformations and constructing new ones.
