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This paper proposes a new discrete-time model reference adaptive controller(MRAC) having new design parameters. In selecting the design parameters, the controller becomes a strongly stable MRAC except the zeros of the plant, that is, the closed-loop system is not only stable, but also the controller itself is stable. The extended MRAC is obtained by including newly introduced design parameters into the controller designed by standard MRAC. The parameters are introduced by applying the coprime factorization approach and comparing Youla-Kucera parametrization of stabilizing compensators to the controller by the standard MRAC.