This study improves an adaptive controller for linear discrete-time plants in two aspects: (1) a new adaptation law is proposed to reduce the residual and the parameter errors; (2) a new method is proposed to modify the parameter estimates if the estimated model is not controllable. The second improvement is required when the plant is non-minimum phase. It obtains a controllable model from available parameter estimates while minimizing the modification offset. These features enhance closed-loop tracking performance of the adaptive controller when it is applied to non-minimum phase plants.