By applying the canonical decomposition of the right invertible system {C, A, B} obtained in Wei, Cheng, and Wang (2010), in this paper we derive a general formula of all solutions to the regular row-by-row decoupling problem. Based on this formula we characterize all attainable transfer function matrices for the decoupling and pole assignment problem in general cases. The results obtained in this paper extend those in the literature. (C) 2012 Elsevier Ltd. All rights reserved.