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The aim of this paper is to deal with the general decoupling problem of linear constant ( ) quadruples from two points of view. The first one is devoted to a characterization of the control laws that decouple quadruples by state feedback, which has been lacking up until now in spite of the results previously obtained by Morse in . Here, we give a complete characterization of solutions by state feedback by means of a necessary and sufficient condition of existence. The second objective of the paper is to check for stability of the closed-loop decoupled system when state feedback is available. This is done in the most general case, i.e., with no particular assumption on the open-loop system as well as on the docoupling partition.