  We study asymptotically non-free gauge theories and search for
renormalization group invariant
  (i.e. technically natural) relations among the couplings which lead to
successful gauge-Yukawa unification. To be definite, we consider a
supersymmetric model based on $SU(4)\times SU(2)_{R}\times SU(2)_{L}$. It is
found that among the couplings of the model, which can be expressed in this way
by a single one in the lowest order approximation, are the tree gauge couplings
and the Yukawa coupling of the third generation. The corrections to the lowest
order results are computed, and we find that the predictions on the low energy
parameters resulting from those relations are in agreement with the
measurements at LEP and Tevatron for a certain range of supersymmetry breaking
scale.
