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In this paper, we evaluate the (second) lightest mass $M_{1,2}$ ofright-handed neutrino $\nu_{R1,2}$ in grand unified theories with the type-Iseesaw mechanism that predicts an almost massless neutrino $m_{1 \, \rm or \,3} \sim 0$. By chiral perturbative treatment, the masses $M_{1,2}$ areexpressed as $M_{1} = m_{D1}^{2}/m_{11} , \, M_{2} = m_{D2}^{2} m_{11} /(m_{11} m_{22} - m_{12}^{2})$ with the mass matrix of left-handed neutrinos $m$in the diagonal basis of the Dirac mass matrix $m_{D}$.  Assuming $m_{Di}$ and the unitary matrix $V$ in the singular valuedecomposition $(m_{D})_{ij} = V_{ik} m_{D k} U^{\dagger}_{kj}$ are close toobserved fermion masses and the CKM matrix, $M_{1,2}$ and their allowed regionsare expressed by parameters in the low energy and unknown phases. As a result,for $m_{D1} \simeq 0.5$ MeV and $m_{D2} \simeq 100$ MeV, we obtain $M_{1}^{\rmNH} \simeq 3 \times 10^{4 - 6}$ GeV and $M_{2}^{\rm NH} \simeq 3 \times10^{6-8}$ GeV in the NH, $M_{1}^{\rm IH} \simeq 5 \times 10^{3 - 4}$ GeV and$M_{2}^{\rm IH} \simeq 4 \times 10^{8-9}$ GeV in the IH. These upper and lowerbounds are proportional to $m_{Di}^{2}$ or $m_{D1} m_{D2}$.

Allowed region for the (second) lightest mass $M_{1,2}$ of right-handed  neutrino $\nu_{R 1,2}$ with $SO (10)$-inspired relations and sequential  dominance