  An arbitrary renormalizable quantum field theory is considered as finite if
its dimensionless couplings conspire to yield, at every order of its
perturbative expansion, no ultraviolet-divergent renormalizations of the
physical parameters of the theory. The "finiteness conditions" resulting from
these requirements form highly complicated, non-linear systems of relations. A
promising type of solution to the condition for one-loop finiteness of the
Yukawa couplings involves Yukawa couplings which are equivalent to the
generators of Clifford algebras with identity element. However, our attempt to
construct even one finite model based on such Clifford-like Yukawa couplings
fails: a Clifford structure of the Yukawa couplings spoils the finiteness of
the gauge couplings, at least for every simple gauge group of rank less than or
equal to 8.
