Motivated by an open problem in the literature “Dynamics of Second Order Rational Difference Equations with Open Problems and Conjecture”, we introduce a difference equation system:

x_n+1={y_n-2+y_n-3}/x_n, y_n+1={x_n-2+x_n-3}/y_n , n=o, 1 ...* Where x_i, y_i ∈（0, ∞）， i=-3, -2, -1, 0.

We try to find out some conditions such that the solution of system converges to periodic solution. This model can be applied to the two species competition and population biology.