  For $\mathcal{N}=1$ supersymmetric Yang-Mills theory without matter it is
demonstrated that there is a class of renormalization schemes, in which the
exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) formula for the
renormalization group $\beta$-function, defined in terms of the renormalized
coupling constant, is valid. These schemes are related with each other by
finite renormalizations forming a one-parameter commutative subgroup of general
renormalization group transformations. The analogy between the exact
$\beta$-function in $\mathcal{N}=1$ supersymmetric Yang-Mills theory without
matter and the $\beta$-function of quantum chromodynamics in the C-scheme is
discussed.
