  In this paper we investigate the renormalization of ${\cal N}=1$
supersymmetric quantum electrodynamics, regularized by higher derivatives, in
the on-shell scheme. It is demonstrated that in this scheme the exact Novikov,
Shifman, Vainshtein, and Zakharov (NSVZ) equation relating the $\beta$-function
to the anomalous dimension of the matter superfields is valid in all orders of
the perturbation theory. This implies that the on-shell scheme enters the
recently constructed continuous set of NSVZ subtraction schemes. To verify this
statement, we compare the anomalous dimension of the matter superfields in the
two-loop approximation and the $\beta$-function in the three-loop
approximation, which are explicitly calculated in this scheme. The finite
renormalizations relating the on-shell scheme to some other NSVZ subtraction
schemes formulated previously are obtained.
