  It is suggested that there is an underlying symmetry which relates the quark
and lepton sectors. Namely, among the mixing matrix elements of CKM for quarks
and PMNS for leptons there exist complementarity relations at a high energy
scale (such as the see-saw or even the GUT scales). Assuming that the relations
would remain during the matrix elements running down to the EW scale.
Observable breaking of the rational relation is attributed to existence of
sterile neutrinos which mix with the active neutrino to result in the
observable PMNS matrix. We show that involvement of a sterile in the (3+1)
model, induces that $|U_{e4}|^2= 0.040$, $|U_{\mu4}|^2= 0.009$ and $\sin^2
2\alpha=0.067$. We also find a new self-complementarity
$\vartheta_{12}+\vartheta_{23}+\vartheta_{13}+\alpha\approx90^\circ$. The
numbers are generally consistent with those obtained by fitting recent
measurements, especially in this scenario, the existence of a sterile neutrino
does not upset the LEP data i.e. the number of neutrino types is very close to
3.
