  We investigate the connection between the NSVZ and the DRED forms of the
gauge $\beta$-function in an $N=1$ supersymmetric gauge theory. We construct a
coupling constant redefinition that relates the two forms up to four loops. By
abelian calculations, we are able to infer the complete non-abelian form of
$\beta_g^{(3)DRED}$, and also $\beta_g^{(4)DRED}$ except for one undetermined
parameter.
