Structure of leptonic Yukawa couplings in the Zee model

The radiative neutrino mass matrix $m^\nu$ in the Zee model depends on leptonic Yukawa couplings $F$ to a singlet scalar and $Y^\ell$ to a new Higgs doublet. Leveraging the skew-symmetric structure of $F$, we derive a unique identity linking $F$ and $m^\nu$ that is explicitly independent of $Y^\ell$. This relation implies that five entries of $Y^\ell$ can, in principle, be determined directly from $m^\nu$ and $F$, while the remaining four can be selected based on phenomenological assumptions. As an illustration, we apply this framework to the two-zero texture $B2$, highlighting its enhancement of the muon $g-2$.