In this paper we examine the model matching problem that concerns non-linear input-output discrete systems, containing products among delays of input and output signals, through a special factorisation. The algebraic framework of -operators and the star-product that we adopt describe these systems. Moreover, a certain procedure that resembles the Euclidean division allows us to discover the linear factors of those systems, with respect to the above mentioned operations. The entire approach is symbolically algorithmic and involves the use of suitable software.