  We develop a method to derive the on-shell invariant quantum action of the
supergravity in such a way that the quartic ghost interaction term is explicity
determined. First, we reinvestigate the simple supergravity in terms of a
principal superfibre bundle. This gives rise to the closed geometrical BRST
algebra. Therefore we determine the open BRST algebra, which realizes the
invariance of the classical action. Then, given a prescription to build the
full quantum action, we obtain the quantum BRST algebra. Together with the
constructed quantum action this allows us to recover the auxiliary fields and
the invariant extension of the classical action.
