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We develop for the CKM and PMNS matrices a new representation with specialproperties. It is obtained by splitting each of these matrices into tworotations by the angle ${\sim}2\pi/3$ and a universal diagonal matrix withelements, which are cubic roots of~1. Such a representation of the CKM and PMNSmatrices may indicate the $Z_{3}$ symmetry to be present in the Yukawa sectorof the~SM. Identical mathematical structure of the CKM and PMNS matrices isalso an extension of the quark-lepton universality. In this approach the CPviolation 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 bythe parameters of two rotations. The parameters of the diagonalizing matricesof the bi-unitary transformation do not exhibit a hierarchy, which means thatthe origins of the hierarchy of quark masses and of the CKM matrix elements arenot the same.

$Z_3$ symmetry of the CKM and PMNS matrices