  Using the Slavnov--Taylor identities we prove that the three-point ghost
vertices with a single line of the quantum gauge superfield are not
renormalized in all loops in ${\cal N}=1$ supersymmetric gauge theories. This
statement is verified by the explicit one-loop calculation made by the help of
the BRST invariant version of the higher covariant derivative regularization.
Using the restrictions to the renormalization constants which are imposed by
the non-renormalization of the considered vertices we express the exact NSVZ
$\beta$-function in terms of the anomalous dimensions of the Faddeev--Popov
ghosts and of the quantum gauge superfield. In the expression for the NSVZ
$\beta$-function obtained in this way the contributions of the Faddeev--Popov
ghosts and of the matter superfields have the same structure.
