A switching scheme for the gain of control variable of a VS-MRAC system was recently presented for plants with relative degree one. In this paper, the scheme is extended to the general case of plants with arbitrary relative degree. By the establishment of the relationship between the tracking error and those auxiliary errors for the case of plants with relative degree greater than one, it is shown that as long as the performance indexes are guaranteed for the auxiliary errors, each of which is in dynamics a subsystem with relative degree one, the tracking error will converge to a small residual set in a prespecified transient time. Furthermore, the influence of averaging filters on the system is analysed and shows that it can be considered as, in a sense, unmodelled dynamics.