  We consider the standard model with two Higgs doublets with the most general
Yukawa coupling terms (``type III''). In the model, the neutral-Higgs-mediated
flavor-changing neutral currents (FCNC's) are allowed, but must be reasonably
suppressed at low energies of probes. It has been known that the existing
hierarchies of quark masses render this suppression at low energies rather
natural. On the other hand, the model has been regarded by many as unnatural
because of the absence of any symmetry that would ensure persistence of this
suppression as the energy of probes increases. The opinion has been based on
the expectation that the mentioned FCNC's would increase by large factors at
increasing energies. We performed a numerical analysis of the flow of these FCN
coupling parameters as governed by the one-loop renormalization group equations
(RGE's), in a simplified case when Yukawa couplings of the first quark
generation are neglected. The analysis shows a remarkable persistence of the
mentioned FCNC suppression and thus indicates that the model is not unnatural
in the RGE sense. Further, we point out two mistakes in the Yukawa RGE's of
Machacek and Vaughn at one-loop level.
