  In this paper it is dealt with the following system of difference equations
  x_{n+1}=((a_{n})/(x_{n}))+((b_{n})/(y_{n})),
y_{n+1}=((c_{n})/(x_{n}))+((d_{n})/(y_{n})), n in N_0,
  where the initial values x_0,y_0 are positive real numbers and the
coefficients (a_{n})_{n>=0}, (b_{n})_{n>=0}, (c_{n})_{n>=0}, (d_{n})_{n>=0} are
two-periodic sequences with positive terms. The system is an extention of a
system that every positive solution is two-periodic or converges to its a
two-periodic solution. Here, the long-term behavior of posistive solutions of
the system is examined by using a new method to solve the system.
