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In this paper, we search for conditions that the mass matrix of lightneutrinos $m_{\nu}$ is not a result of large cancellations for the type-Iseesaw mechanism with four-zero texture. For the Yukawa matrix of neutrinos$Y_{\nu}$ and heavy Majorana mass matrix $M_{R}$, these conditions are writtenas $(Y_{\nu})_{i2} \propto (m_{\nu})_{i2} \, \Rightarrow \, (Y_{\nu})_{i2}\propto (M_{R})_{i2}$. We call them {\it alignment} conditions because theyalign the certain rows or columns of the three neutrino mass matrices. If theseconditions do not hold, the large mixing in $m_{\nu}$ is a result offine-tuning due to the cancellation of several terms. Then they are requiredfrom a viewpoint of naturalness.  They give an explanation of the seesaw-invariance of four-zero texture, andplace rough restrictions on flavor structures of neutrinos. Under theseconditions, $Y_{\nu}$ must have a cascade hierarchy. For $M_{R}$, the 12submatrix has a similar hierarchy as $Y_{\nu}$ and $m_{\nu}$. However, the 23submatrix has a waterfall hierarchy without some fine-tuning. Therefore, it islikely that $Y_{\nu}$ and $M_{R}$ have qualitatively different flavorstructures. Furthermore, since the conditions restrict CP phases of the matrixelements, they imply existence of a universal generalized CP symmetry in theneutrino sector.

Conditions of naturalness and fine-tunings for type-I seesaw mechanism with four-zero texture