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This paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay x (k+ 1)= A x (k)+ B x (k− m), k= 0, 1,… where A, B are square constant matrices and m∈ N. Sufficient conditions for exponential stability are derived using the method of Lyapunov functions and its efficiency is demonstrated by examples.