The paper aims to study the dynamics of a system of nonlinear difference equations x(n+1) = x(n-1)y(n) + A, y(n+1) = y(n-1)x(n) + A where is real number. We especially investigate the stability of equilibrium points, convergence of equilibrium points, existence of periodic solutions, and existence of bounded solutions of related system. Moreover, we present some numerical examples to verify the theoretical results