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We propose a new pattern of the neutrino mixing matrix which can beparametrized as the product of an arbitrary Hermitian matrix and the well-knowntri-bimaximal mixing matrix. In this scenario, nontrivial values of thesmallest neutrino mixing angle \theta_13 and the CP-violating phases entirelyarise from the non-unitary corrections. We present a complete set of seriesexpansion formulas for neutrino oscillation probabilities both in vacuum and inmatter of constant density. We do a numerical analysis to show the non-unitaryeffects on neutrino oscillations. The possibility of determining smallnon-unitary perturbations and CP-violating phases is discussed by measuringneutrino oscillation probabilities and constructing "deformed unitaritytriangles". Some brief comments on the non-unitary neutrino mixing matrix inthe type-II seesaw models are also given.

Non-unitary deviation from the tri-bimaximal lepton mixing and its implications on neutrino oscillations