  For the ${\cal N}=1$ supersymmetric electrodynamics we investigate
renormalization schemes in which the NSVZ equation relating the
$\beta$-function to the anomalous dimension of the matter superfields is valid
in all loops. We demonstrate that there is an infinite set of such schemes.
They are related by finite renormalizations which form a group and are
parameterized by one finite function and one arbitrary constant. This implies
that the NSVZ $\beta$-function remains unbroken if the finite renormalization
of the coupling constant is related to the finite renormalization of the matter
superfields by a special equation derived in this paper. The arbitrary constant
corresponds to the arbitrariness of choosing the renormalization point. The
results are illustrated by explicit calculations in the three-loop
approximation.
