In this paper, structured systems described by state-space models are considered. I;or these systems, the entries of the state space model matrices are assumed to be either fixed zeros or free independent parameters, The authors study the dynamic decoupling of structured linear systems. It turns out that a large class of systems which is not state feedback decouplable can be made decouplable by the addition of a simple structured precompensator. Such a precompensator then has the property to be independent of the system parameters. In this paper the authors give a necessary and sufficient condition for a structured system to be made feedback decouplable using a parameter independent precompensator, Furthermore, they prove that when such a solution exists, the precompensator can he chosen to be diagonal. In this case the precompensator is constructed via a simple combinatorial algorithm. Our approach is based on a graph representation of the structured system, All the results of this paper are related to some particular shortest sets of input-output paths in the graph associated with the structured system.