Suppose that A(n) is an almost periodic matrix function of the integer variable n, that A(n) is invertible for each \(n\in Z\) and that \(A^{- 1}(n)\) is bounded on Z. Then it is proved that if the linear difference equation \(x(n+1)=A(n)\times (n)\) has an exponential dichotomy on a set \(\{m,m+1,...,m+T\}\) of consecutive integers with T sufficiently large, then it has an exponential dichotomy on all of Z. The results obtained are discrete analogues of the corresponding results of K. J. Palmer [Proc. Am. Math. Soc. 101, 293-298 (1987; Zbl 0664.34016)].