respectively. In this basis, we impose and We note that with Eq. (8), the down-type quark mass matrix becomes similar to the hy- brid texture discussed in Ref. [17]. On the other hand, the up-type one is almost diagonal. Since M u,d are real and symmetric matrices, they can be diagonalized by real orthogonal matrices: V T q M $^{q}$V$_{q}$ = diag( m$_{q}$ 1 , m$_{q}$ 2 , m$_{q}$ 3 ). With Eq. (8), V$_{q}$ can approximately be written as with m$_{u}$/m$_{c}$ ≃ η 2 u and m$_{c}$/m$_{t}$ ≃ | ξ$_{u}$ | for the up-quark sector, and with m$_{d}$/m$_{s}$ ≃ η 2 d and m$_{s}$/m$_{b}$ ≃ 1 / 2 | ξ$_{d}$ | for the down-quark sector, respectively. Note that the factor 1 / 2 in Eq. (10) arises from the { 33 } element of Eq. (7). From the mass ratios, we can deduce that with λ ≃ 0 . 22. Therefore, in what follows, we consider the following hierarchical FL translation: 4 d$_{i}$ → d$_{i}$ + (1 , λ, λ $^{3}$) $^{T}$z$_{d}$ . (14) u$_{i}$ → u$_{i}$ + (1 , − λ $^{2}$, − λ $^{6}$) $^{T}$z$_{u}$ , (13) | η$_{d}$ | ≃ λ, | ξ$_{d}$ | ≃ λ $^{2}$, (12) | η$_{u}$ | ≃ λ $^{2}$, | ξ$_{u}$ | ≃ λ $^{4}$, (11) V$_{d}$ ≃    1 − η$_{d}$ − 1 $_{2}$η$_{d}$ ξ$_{d}$ η$_{d}$ 1 − 1 $_{2}$ξ$_{d}$ η$_{d}$ξ$_{d}$ 1 $_{2}$ξ$_{d}$ 1    (10) V$_{u}$ ≃    1 − η$_{u}$ 0 η$_{u}$ 1 0 0 0 1    (9) A$_{q}$ ≃ B$_{q}$ ≃ C$_{q}$ and η$_{q}$, ξ$_{q}$ ≪ 1 . (8) M d =    ( B$_{d}$ + C$_{d}$ξ$_{d}$ ) η 2 d − B$_{d}$η$_{d}$ − C$_{d}$η$_{d}$ − B$_{d}$η$_{d}$ A$_{d}$ξ$_{d}$ + B$_{d}$ − A$_{d}$ − C$_{d}$η$_{d}$ − A$_{d}$ ( A$_{d}$ + C$_{d}$ ) /ξ$_{d}$   $^{,}$ (7)