  Recently the exact NSVZ $\beta$-function was rewritten in the form of a
relation between the $\beta$-function and the anomalous dimensions of the
quantum gauge superfield, of the Faddeev--Popov ghosts, and of the matter
superfields. It was also suggested that this form of the NSVZ equation follows
from an underlying equation relating two-point Green functions of the theory.
Here we demonstrate that this relation is satisfied at the two-loop level for
the non-Abelian ${\cal N}=1$ supersymmetric gauge theories in the case of using
the simplest (BRST non-invariant) version of the higher covariant derivative
regularization. Consequently, the integrals giving the two-loop
$\beta$-function can be reduced to the one-loop integrals giving the anomalous
dimensions of the quantum gauge superfield, of the Faddeev--Popov ghosts, and
of the matter superfields.
