This paper is concerned with difference equation $ y(n+1) = A_ny_n+f(n, \, y_{n+\delta_n}, \lambda) infinite delay in a Banach space X $, where \delta_n ($ n\in {\mathbb Z} $) given sequence taking values \{0, 1\} and \lambda parameter. First, we construct Lipschitz invariant manifold {\mathcal M}^{\lambda} of the which consists all bounded forward solutions. Then prove that contains unique com...