This paper proposes a new robust adaptive beamformer suitable for a two-channel microphone array. The proposed beamformer is a combination of two Griffith-Jim generalized sidelobe cancellers (GSC) in which the look direction of each GSC is determined by the other GSC's directional response. Moreover, to reduce the degradation of interference suppression performance caused by spatial aliasing, a new arrangement of directional microphones is proposed. The arrangement is simple and effectively reduces the degradation. Simulations demonstrate the effectiveness of the proposed two- channel two-beamformer microphone array.