In this paper, we continue the work in Malabre and Velasquez (Decoupling of linear systems by means of proportional and derivative state feedback, Proceedings of the SCI'94, Wuhan, China, 1994) and Bonilla Estrada and Malabre (IEEE Trans. Automat. Control 45 (2000) 730) and study the row-by-row decoupling problem of linear time-invariant systems by proportional and derivative state feedback. Our contribution, with respect to previous results, is that we develop a numerical method to compute the desired feedback matrices. Our numerical method is only based on orthogonal transformations and hence is numerically reliable.