On the system of difference equations xn=cnyn-3/(an+bnyn-1xn-2yn-3)xn=cnyn-3/(an+bnyn-1xn-2yn-3), yn=γnxn-3/(αn+βnxn-1yn-2xn-3)yn=γnxn-3/(αn+βnxn-1yn-2xn-3)

We show that the system of difference equationsxn=cnyn-3an+bnyn-1xn-2yn-3,yn=γnxn-3αn+βnxn-1yn-2xn-3,n∈N0,where the sequences anan, bnbn, cncn, αnαn, βnβn, γnγn, n∈N0n∈N0, and initial values x-ix-i, y-iy-i, i∈{1,2,3}i∈{1,2,3} are real numbers, such that cn≠0, γn≠0, n∈N0n∈N0, can be solved in closed form, and for the case when all the sequences anan, bnbn, cncn, αnαn, βnβn and γnγn are constant we describe the asymptotic behavior of well-defined solutions of the system.