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Stereophonic acoustic echo cancellers (SAEC) have problems more severe than monophonic echo cancellers. The most important problem is the misalignment, which is the mismatch between the impulse responses of adaptive filters and those of the acoustic paths of the receiving room (in the teleconferencing application, as an example) and therefore a severe divergence of filters in the event of abrupt changes of the transmission room acoustic paths. The main reason for such mismatching is the two-channel nature of the system and the high degree of cross-correlation of the input signals of those channels. In this paper, we try to reduce the correlation between the two channels in the transform domain. To achieve this, with inspiration from the lattice predictor structure, we present a novel approach for reduction of cross-correlation of the input vectors of two channels in the wavelet domain that lead to a reduction in the misalignment of adaptive filters for the SAEC.