We give the necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation $x_{n+1};-;a^2x_{n-1};+;bx_{n-k};=;0$, n = 0, 1,$cdots$, where a and b are arbitrary real numbers and k is a positive integer greater than 1. The obtained conditions are given in terms of parameters a and b of difference equations. The method of proof is based on arithematic of complex numbers as well as properties of analytic functions.