In this paper, a new spectral subtraction technique with two microphone inputs is proposed. In conventional spectral subtraction using a single microphone, the averaged noise spectrum is subtracted from the observed short-time input spectrum. This results in reduction of mean value of noise spectrum only, the component varying around the mean value remaining intact. In the method proposed in this paper, the short-time noise spectrum excluding the speech component is estimated by introducing the blocking matrix used in the Griffiths-Jim-type adaptive beamformer with two microphone inputs, combined with the spectral compensation technique. By subtracting the estimated short-time noise spectrum from the input spectrum, not only the mean value of the noise spectrum but also the component varying around the mean value can be reduced. This method can be interpreted as a partial construction of the adaptive beamformer where only the amplitude of the short-time noise spectrum is estimated, while the adaptive beamformer is equivalent to the estimator of the complex short-time noise spectrum. By limiting the estimation to the amplitude spectrum, the proposed system achieves better performance than the adaptive beamformer in the case when the number of sound sources exceeds the number of microphones.