  In this paper, we consider a set of new symmetries in the SM, {\it diagonal
reflection} symmetries $R \, m_{u,\nu}^{*} \, R = m_{u,\nu}, ~ m_{d,e}^{*} =
m_{d,e}$ with $R =$ diag $(-1,1,1)$. These generalized $CP$ symmetries predict
the Majorana phases to be $\alpha_{2,3} /2 \sim
  0$ or $\pi /2$.
  A realization of reflection symmetries suggests a broken chiral $U(1)_{\rm
PQ}$ symmetry and a flavored axion. The axion scale is suggested to be $\langle
\theta_{u,d} \rangle \sim \Lambda_{\rm GUT} \, \sqrt{m_{u,d} \, m_{c,s}} / v
\sim 10^{12} \, $[GeV].
  By combining the symmetries with the four-zero texture, the mass eigenvalues
and mixing matrices of quarks and leptons are reproduced well. This scheme
predicts the normal hierarchy, the Dirac phase $\delta_{CP} \simeq
203^{\circ},$ and $|m_{1}| \simeq 2.5$ or $6.2 \, $[meV].
  In this scheme, the type-I seesaw mechanism and a given neutrino Yukawa
matrix $Y_{\nu}$ completely determine the structure of right-handed neutrino
mass $M_{R}$. An $u-\nu$ unification predicts mass eigenvalues to be $ (M_{R1}
\, , M_{R2} \, , M_{R3}) = (O (10^{5}) \, , O (10^{9}) \, , O (10^{14})) \,
$[GeV].
