In this paper, we consider discrete time dissipativeness on quadratic difference forms and two-variable dipolynomial matrices. We show that if a system is dissipativeness for a supply rate on the dipolynomial ring, then there also exist storage functions and dissipation rates on the dipolynomial ring. Moreover, we clarify whether extremal storage functions for a given supply rates on the dipolynomial ring. This generalization is effective to extend dissipation theory in discrete time from the theoretical points of view.