  We develop for the CKM and PMNS matrices a new representation with special
properties. It is obtained by splitting each of these matrices into two
rotations by the angle ${\sim}2\pi/3$ and a universal diagonal matrix with
elements, which are cubic roots of~1. Such a representation of the CKM and PMNS
matrices may indicate the $Z_{3}$ symmetry to be present in the Yukawa sector
of the~SM. Identical mathematical structure of the CKM and PMNS matrices is
also an extension of the quark-lepton universality. In this approach the CP
violation is a natural consequence of the structure of the Yukawa couplings.
The CP violating phase is not a fitted parameter and its value is governed by
the parameters of two rotations. The parameters of the diagonalizing matrices
of the bi-unitary transformation do not exhibit a hierarchy, which means that
the origins of the hierarchy of quark masses and of the CKM matrix elements are
not the same.
