The recent observational data supports the deviation from Tri-bimaximal (TBM) mixing. Different theories suggest the interdependency among the observational parameters involving the mixing angles. On phenomenological ground, we try to construct the PMNS matrix, U_PMNS with certain analytic structure satisfying spontaneously the unitary condition, in terms of a single observational parameter sinθ₁₃ We hypothesise the three neutrino masses, m_i as functions of sinθ₁₃ and then construct the neutrino mass matrix M_v with certain exact and expandable form. We assume the convergence of the model to TBM mixing when θ₁₃ is taken 0. The mass matrix so far obtained can be employed for various applications including the estimation of matter-antimatter asymmetry of the universe.