The minus signs in the up sector come from η$_{u}$ which is negative to reproduce realistic CKM elements. We note that although the up and down quarks are massless at this stage, in the above approximation, we remain m$_{u}$ and m$_{d}$ to be nonzero in order to determine the order of η$_{q}$ . The parameters η$_{u}$ = − λ 2 and η$_{d}$ = λ would be the origin of m$_{u}$/m$_{c}$ ∼ λ 4 and m$_{d}$/m$_{s}$ ∼ λ $^{2}$, respectively, when we introduce the symmetry breaking terms. On the other hand, the parameters η$_{q}$ and ξ$_{q}$ can also be the origin of the tiny mixing angles of the CKM matrix. For instance, three elements of the CKM matrix can be estimated as where we have used λ ≃ 4 λ $^{2}$. These results well coincide with the experimental values θ 12 ≃ λ, θ 23 ≃ λ $^{2}$, and θ 13 ≃ λ 4 mentioned in the Introduction. Namely, in our model, the flavor structures in the quark sector are explained by the hierarchical patterns of the symmetry. Hence, it is also easy to establish the relations between the masses and mixing angles, such as via ξ$_{d}$ , respectively. via η$_{d}$ , and In order to generate the light quark masses, the FL symmetry must be broken. Since we do not know the origin of the breaking, there may exist many possible ways to break the symmetry. Here, we aim at a minimal scheme and put phase factors into the mass matrices to break the FL and CP symmetries simultaneously as discussed in Ref. [10]. 5 III. FL SYMMETRY BREAKING AND PARAMETER FITTING | V$_{us}$ | ≃ | − η$_{d}$ + η$_{u}$ | ≃ 1 . 25 λ, | V$_{ub}$ | ≃ 0 . 5 | − η$_{d}$ξ$_{d}$ − η$_{u}$ξ$_{d}$ | ≃ 1 . 5 λ $^{4}$, (15) | V$_{cb}$ | ≃ 0 . 5 | ξ$_{d}$ | ≃ 0 . 5 λ $^{2}$, √ m$_{d}$/m$_{s}$ ∼ | V$_{us}$ | (16) m$_{s}$/m$_{b}$ ∼ | V$_{cb}$ | (17)