This paper presents new superdirective beamforming algorithms based on the maximum negentropy (MN) criterion for distant automatic speech recognition. The MN beamformer is configured in the generalized sidelobe canceler structure, and uses the weights derived from a delay-and-sum beamformer as the quiescent weight vector. While satisfying the distortionless constraint in the look direction, it adjusts the active weight vector to make the output maximally super-Gaussian. The current paper proposes to use the weights of a superdirective beamformer as the quiescent vector, which results in improved directivity and noise suppression at lower frequencies. We demonstrate the effectiveness of our approach through far-field speech recognition experiments on the Multi-Channel Wall Street Journal Audio Visual Corpus (MC-WSJ-AV). The technique proposed in the current paper reduces the word error rate (WER) by 56% relative to a single distant microphone baseline, which is a 14% reduction in WER over the original MN beamformer formulation.