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Stereophonic acoustic echo cancellation (SAEC) plays an important role in delivering realistic teleconferencing experience. The fundamental problem of SAEC system is that stereophonic channels are linearly related and this results in slow convergence of the adaptive filters. In this paper, we present a novel algorithm by employing a selective time-reversal block to solve the SAEC problem which results in a significant increase in the convergence performance of adaptive filters such that the stereophonic image as well as quality are preserved. The proposed algorithm employs time-reversal operation on selective blocks of input data samples for one of the two channels to decorrelate stereophonic channels in the SAEC system. To achieve good stereophonic perception, time-reversal operation is only applied to the selective blocks whose magnitudes fall below a pre-determined threshold. Theoretical and numerical simulation results are also studied and investigated to show that the proposed algorithm achieves faster convergence in terms of normalized misalignment and better stereophonic perception with less audio distortion compared to the well-known nonlinear transformation algorithm for the SAEC system.