  We verify a recently proposed method for obtaining a $\beta$-function of
${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives by
an explicit calculation. According to this method, a $\beta$-function can be
found by calculating specially modified vacuum supergraphs instead of a much
larger number of the two-point superdiagrams. The result is produced in the
form of a certain integral of double total derivatives with respect to the loop
momenta. Here we compare the results obtained for the three-loop
$\beta$-function of ${\cal N}=1$ SQED in the general $\xi$-gauge with the help
of this method and with the help of the standard calculation. Their coincidence
confirms the correctness of the new method and the general argumentation used
for its derivation. Also we verify that in the considered approximation the
NSVZ relation is valid for the renormalization group functions defined in terms
of the bare coupling constant and for the ones defined in terms of the
renormalized coupling constant in the HD+MSL scheme, both its sides being
gauge-independent.
