  By use of the one-loop renormalization group equations and current
experimental data, we study the off-diagonal asymmetries of the
Cabibbo-Kobayashi-Maskawa (CKM) matrix at the GUT scale in the framework of the
standard model as well as its two Higgs and supersymmetric extensions. It is
concluded that the possibility of a symmetric CKM matrix at the GUT scale has
almost been ruled out.
