In this paper we present a solution to the problem of designing a globally convergent adaptive decoupling controller for multiinput/multioutput linear time invariant continuous-time systems with unknown (possibly nondiagonal) interactor matrix. The only assumptions about the plant are that it is minimum phase and that an upper bound on its McMillan degree and the relative degrees of each of the entries of its transfer matrix are known. The decoupling is minimal in the sense that asymptotic tracking is achieved with the minimal infinity structure, i.e., the smallest number of integrators. Instrumental for our analysis are the utilization of Morse’s new dynamic certainty equivalent adaptive controller and the output reordering procedure proposed by Mutoh and Ortega to estimate the interactor structure.