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We find the three-loop contribution to the $\beta$-function of ${\cal N}=1$supersymmetric gauge theories regularized by higher covariant derivativesproduced by the supergraphs containing loops of the Faddeev--Popov ghosts. Thisis done using a recently proposed algorithm, which essentially simplifies suchmultiloop calculations. The result is presented in the form of an integral ofdouble total derivatives in the momentum space. The considered contribution tothe $\beta$-function is compared with the two-loop anomalous dimension of theFaddeev--Popov ghosts. This allows verifying the validity of the NSVZ equationwritten as a relation between the $\beta$-function and the anomalous dimensionsof the quantum superfields. It is demonstrated that in the consideredapproximation the NSVZ equation is satisfied for the renormalization groupfunctions defined in terms of the bare couplings. The necessity of thenonlinear renormalization for the quantum gauge superfield is also confirmed.

Three-loop contribution of the Faddeev-Popov ghosts to the $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories and the NSVZ relation