  We demonstrate that in the $P=\frac{1}{3}Q$ supersymmetric theories the
renormalization group invariance of the ratio $\lambda^{ijk}/e$ (of the Yukawa
couplings to the gauge coupling) is equivalent to a simple relation between the
anomalous dimensions of the quantum gauge superfield, of the Faddeev--Popov
ghosts, and of the matter superfields, which should be valid in each order of
the perturbation theory. In the one- and two-loop approximations it is verified
explicitly. Presumably, in higher orders this relation can be satisfied for the
planar supergraphs under a certain renormalization prescription. Assuming that
it is valid we rewrite the exact equation for the (corresponding contribution
to the) anomalous dimension of the matter superfields in the theories under
consideration in a different (but equivalent) form.
