In this paper, a multi-microphone noise reduction system based on the generalized sidelobe canceller (GSC) structure is investigated. The system consists of a fixed beamformer providing an enhanced speech reference, a blocking matrix providing a noise reference by suppressing the target speech, and a single-channel spectral post-filter. The spectral post-filter requires the power spectral density (PSD) of the residual noise in the speech reference, which can in principle be estimated from the PSD of the noise reference. However, due to speech leakage in the noise reference, the noise PSD is overestimated, leading to target speech distortion. To minimize the influence of the speech leakage, a maximum noise-to-speech ratio (MaxNSR) blocking matrix is proposed, which maximizes the ratio between the noise and the speech leakage in the noise reference. The proposed blocking matrix can be computed from the generalized eigenvalue decomposition of the correlation matrix of the microphone signals and the noise coherence matrix, which is assumed to be time-invariant. Experimental results in both stationary and nonstationary diffuse noise fields show that the proposed algorithm outperforms existing blocking matrices in terms of target speech blocking ability, noise estimation and noise reduction performance.