The binary model reference adaptive control (B-MRAC) is a controller combining the good transient and robustness of Sliding Mode Control (SMC) with the smoothness of parameter adaptive control. The B-MRAC delivers continuous control signal being able to mitigate SMC chattering problems. As the adaptation gain increases, the B-MRAC tends to behave as the SMC. However, the residual set input perturbations was only shown to bounded but the bound was not shown to tend to zero as the gain increased without limit as expected for the SMC. In this paper we show that this property indeed holds and the residual error tends to zero as the adaptation gain increases to infinity. Simulation results illustrate the consistency of the theory presented.