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This correspondence proposes a new block-exact fast least-mean squares (LMS)/Newton algorithm for adaptive filtering. It is obtained by exploiting the shifting property of the whitened input of the fast LMS/Newton algorithm so that a block-exact update can be carried out in the LMS part of the algorithm. The proposed algorithm has significantly less computational complexity than, but exact mathematical equivalence to, the fast LMS/Newton algorithm. Since short block length is allowed, the processing delay introduced is not excessively large as in conventional block filtering generalization. Implementation issues and the experimental results are given to illustrate the principle and efficiency of the proposed algorithm.