In this paper, we present a novel single-input/binaural-output (SIBO) minimum variance distortionless response (MVDR) noise reduction method, which involves formulating two MVDR sub-filters, one for the left ear and the other for the right ear, by minimizing the interaural coherence of the noise signal while ensuring the distortionless constraint, so that the desired speech signal can pass through the filter without distortion. Subsequently, a unique heterophasic binaural presentation is generated. The method effectively reduces noise while directing the desired signal and residual noise to different directions/zones in the perceptual space. This utilization of human binaural perception properties enhances speech intelligibility. A deep neural network (DNN) based noise covariance matrix estimation method facilitates the implementation of the binaural heterophasic filters in simulations and listening tests. The results demonstrate the superiority of the proposed SIBO MVDR method in enhancing both speech quality and intelligibility as compared to the conventional single-input/single-output (SISO) MVDR filter.