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In this paper, we investigate the form of the solutions of the following systems of difference equations of second order xn+1xn+1==xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xnyn−1xn−yn,yn+1=xn−1ynxn−yn,   n=0,1,...,xn+1=xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xn+1=xnyn−1xn−yn,yn+1=xn−1ynxn−yn,   n=0,1,..., where the initial conditions x−1, x0, y−1 x−1, x0, y−1  and  y0 y0 are arbitrary nonzero real numbers.