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We consider an expansion of the type-I seesaw mechanism by the inverse of the3-3 matrix element $1/(M_{R})_{33}$ of the mass matrix of right-handedneutrinos $M_{R}$. Conditions of such a situation are obtained for $M_{R}$ andthe Dirac mass matrix $m_{D}$.  In this case, a partial $Z_{2}$ symmetry such as $S m_{D} P_{} = \pm m_{D}P_{}$ with a projection matrix $P_{} = {\rm diag} ( 1, 1, 0)$ leads to anapproximate $Z_{2}$ symmetry by $S$ for the neutrino mass matrix $m_{\nu}$.Such a partial $Z_{2}$ symmetry is desirable in the context of unified theoriesbecause it allows hierarchical $m_{D}$ and the large mixing of $m_{\nu}$simultaneously.

$1/(M_{R})_{33}$ expansion of the type-I seesaw mechanism and partial $Z_{2}$ symmetry for TM$_{1,2}$ mixing