In this paper, the decoupling problems by dynamic output feedback and constant precompensator are considered under the constraint of weak or strong internal stability. This problem has been first considered by Hammer and Khargonekar (1984) for systems with square transfer matrices. Here, the problem is taken up in a more general setting and it is only assumed that transfer matrix has full row rank. In this respect, the problem being considered is the same as the one considered in Eldem (1994-a) except the constraint of internal stability. It is shown that the recently introduced notions of diagonal stability and causality degree dominance and the joint essential stability functions (Eldem (1994-b)) play a central role in the solution of the problem. Moreover, using the latter, one can obtain a characterization of all solutions if the constant precompensator part of the control is known.