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Abstract: It is well known that the tri-bimaximal neutrino mixing pattern can be derived from a class of flavor models with the non-Abelian symmetry. We point out that small corrections to , which are inherent in the models and arise from both the charged-lepton and neutrino sectors, have been omitted in the previous works. We show that such corrections may lead the neutrino mixing matrix V to a non-unitary deviation from , but they cannot result in a nonzero value of or any new CP-violating phases. Current experimental constraints on the unitarity of V allow us to constrain the model parameters to some extent. [Copyright &y& Elsevier]