  We consider a situation where the leading-order neutrino mass matrix is
derived by a theoretical ansatz and reproduces the experimental data well, but
not completely. Then, the next stage is to try to fully reproduce the data by
adding small perturbation terms. In this paper, we obtain the analytical method
to diagonalize the perturbed mass matrix and find a consistency condition that
parameters should satisfy not to change \sin\theta_{12} much. This condition
could cause parameter tuning and plays a crucial role in relating the added
perturbation terms with the prediction analytically, in particular, for the
case of the partially quasi-degenerated neutrino masses (m_2 \simeq m_1) where
neutrinoless double beta decays would be observed in the phase-II experiments.
