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We study the case of $U^T_l$ presenting the exact bi-maximal mixing form with$U_\nu$ inducing the deviation from the bi-maximal mixing in the final form ofthe Pontecorvo-Maki-Nakagawa-Sakata neutrino mixing, $U_{PMNS}=U^T_l U_\nu$. Wewill show that such possibility will lead to a democratic texture for thecharged lepton mass matrix and to a neutrino mass matrix with four nullentries.Comment: a scenario realizing our proposal is added, new references added, to  be published in J.Phys.

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