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We analyze the radiative leptonic Be decay B-→τ-(v)τγ in the Standard Model and the twoHiggs-doublet model using the non-relativistic constituent quark model.The results confirm that this channel is experimentally promising in view of the large number of Bc mesons which are expected to be produced at future hadron facilities.We also find that this decay is sensitive to the parameters of the two-Higgs-doublet model,and it can be tested in future experiments.