A solution is presented to the long-standing open problem of linear systems theory-diagonal decoupling by static-state feedback. The earliest known investigation of system decoupling dates back to 1934, a state-space formulation of the problem appeared in 1964, and a solution for square and invertible systems followed in 1967. The case of right-invertible systems, however, has withstood all past efforts to obtain a solution save for several special cases. The present formulation avoids restrictive hypotheses concerning system and decoupling feedback. The existence of a solution is shown to depend on the existence of three lists of integers conditioned solely by system invariants with respect to the permissible transformations.