Stereophonic acoustic echo cancellers are being used in high quality audio communication systems to reduce the echoes that arise from coupling between the loudspeakers and microphones. These echo cancellers have problems more severe than their monophonic counterparts. The most important problem is the mismatch between the impulse responses of adaptive filters and those of the acoustic paths of the receiving section and therefore a severe divergence of filters in the event of abrupt changes of the transmission section acoustic paths. The main reason for such mismatching is the two-channel nature of the system and strong cross-correlation between these two channels. In this paper, with inspiration from the lattice predictor structure, we present a novel approach for reduction of the interchannel cross-correlation of the input vectors in the wavelet domain that leads to faster reduction of the misalignment error.