  We discuss a discrete approach to the multiscale reductive perturbative
method and apply it to a biatomic chain with a nonlinear interaction between
the atoms. This system is important to describe the time evolution of localized
solitonic excitations. We require that also the reduced equation be discrete.
To do so coherently we need to discretize the time variable to be able to get
asymptotic discrete waves and carry out a discrete multiscale expansion around
them. Our resulting nonlinear equation will be a kind of discrete Nonlinear
Schr\"odinger equation. If we make its continuum limit, we obtain the standard
Nonlinear Schr\"odinger differential equation.
