Many studies have used motor imagery-based brain-computer interface (MI-BCI) systems for stroke rehabilitation to induce brain plasticity. However, they mainly focused on detecting motor imagery but did not consider the effect of false positive (FP) detection. The FP could be a threat to patients with stroke as it can induce wrong-directed brain plasticity that would result in adverse effects. In this study, we proposed a rehabilitative MI-BCI system that focuses on rejecting the FP. To this end, we first identified numerous electroencephalogram (EEG) signals as the causes of the FP, and based on the characteristics of the signals, we designed a novel two-phase classifier using a small number of EEG channels, including the source of the FP. Through experiments with eight healthy participants and nine patients with stroke, our proposed MI-BCI system showed 71.76% selectivity and 13.70% FP rate by using only four EEG channels in the patient group with stroke. Moreover, our system can compensate for day-to-day variations for prolonged session intervals by recalibration. The results suggest that our proposed system, a practical approach for the clinical setting, could improve the therapeutic effect of MI-BCI by reducing the adverse effect of the FP.