ABSTRACT.In this paper, we get the form of the solutions of the following difference equation systems of order four\[z_{n+1} = \frac{z_{n}w_{n-2}}{\,w_{n-2} + w_{n-3}\,},\qquadw_{n+1} = \frac{w_{n}z_{n-2}}{\,\pm z_{n-2} \pm z_{n-3}\,},\]where the initial conditions \( z_{-3}, z_{-2}, z_{-1}, z_{0}, w_{-3}, w_{-2}, w_{-1}, w_{0} \) are arbitrary non-zero real numbers.