In adaptive control systems, it is a difficult task to choose an adequate reference model such that the perfect model matching condition can be guaranteed in every adaptive step. This paper presents a new design algorithm for model reference adaptive control systems to synthesize an adaptive controller such that the output error between the reference model and the plant can vanish in a minimax manner, which can improve the transient behaviour of model reference adaptive control systems. In this situation, the stringent matching condition can be relaxed; therefore, the proposed design algorithm is also suitable for unstable or non-minimum phase systems. A series of computer simulations is also included to illustrate the proposed design algorithm.