It is shown that from the linearized Slavnov identity introduced in an earlier paper [2] it follows that the effective Lagrangian of the regularized theory can be reduced to a BRST-invariant form by a certain special linear transformation of the fields. Technically, the proof of the corresponding theorem requires the introduction of a new system of ghosts. The new ghosts make it possible, in particular, to interpret the original symmetry condition nonperturbatively.