In a related article, we derived a canonical decomposition of the right invertible system (C, A, B) and applied this canonical decomposition to study the Smith form of the matrix pencil P(s) = ((A - sl)(C) (B)(0)) and findout the finite zeros and infinite zeros of P(s), the range of the ranks of P(s) for s is an element of C, and the controllability of the right invertible system. In this paper, we will apply this canonical decomposition of the right invertible system (C, A. B) to deduce the triangular decouple upon to row permutation, provide some new results of the row-by-row decoupling, and associated pole assignment problems. (C) 2010 Elsevier Ltd. All rights reserved.