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In the supersymmetric left-right model,the light neutrino masses are given by the Type-II seesaw mechanism.A duality property of this mechanism indicates that there exist eight possible Higgs triplet Yukawa couplings which result in the same neutrino ma6s matrix.In this paper,we work out the one-loop renormalization group equations for the effective neutrino mass matrix in the supersymmetric left-right model.The stability of the Type-II seesaw scenario is briefly discussed.We also study the lepton-flavor-violating processes (τ→μγ and τ→eγ)by using the reconstructed Higgs triplet Yukawa couplings.