In this note we show the the system of difference equationswhere n ∈ N 0 , the initial values x −2 , x −1 , x 0 , y −2 , y −1 and y 0 are arbitrary nonzero real numbers and the parameters a, b, c and d are arbitrary real numbers with d = 0, can be solved in a closed form. We will see that when a = b = c = d = 1 the solutions are expressed using the famous Teteranacci numbers. In particular, the results obtained here extend those in our work [1].