In the design of multi-input multi-output (MIMO) adaptive control systems an interactor plays an important role. The derivation of the interactor requires system parameter values unless the interactor is in diagonal form. This is a considerable restriction when the interactor is applied to the adaptive control system design. In MIMO adaptive control many parameters must be estimated to achieve good tracking. Over-parametrization causes many problems, e.g. bad tracking performance and long calculation time of control input. A design of interactor, called a G-interactor, for unknown MIMO plants is given. It is applied to MIMO adaptive control systems. The G-interactor requires minimum information on the plant, such as the relative degree of each element of the plant transfer matrix. For this design a canonical form, called the G-canonical form, of a matrixAis investigated. The canonical form is also used to eliminate redundant parameters of MIMO adaptive control systems. Numerical examples show the effectiveness of the proposed adaptive control design.