  We derive the one loop renormalization group equations for the
Cabibbo-Kobayashi-Maskawa matrix for the Standard Model, its two Higgs
extension and the minimal supersymmetric extension in a novel way. The derived
equations depend only on a subset of the model parameters of the
renormalization group equations for the quark Yukawa couplings so the CKM
matrix evolution cannot fully test the renormalization group evolution of the
quark Yukawa couplings. From the derived equations we obtain the invariant of
the renormalization group evolution for three models which is the angle
$\alpha$ of the unitarity triangle. For the special case of the Standard Model
and its extensions with $v_{1}\approx v_{2}$ we demonstrate that also the shape
of the unitarity triangle and the Buras-Wolfenstein parameters
$\bar{\rho}=(1-{1/2}\lambda^{2})\rho$ and $\bar{\eta}=(1-{1/2}\lambda^{2})\eta$
are conserved. The invariance of the angles of the unitarity triangle means
that it is not possible to find a model in which the CKM matrix might have a
simple, special form at asymptotic energies.
