  We study the invariance of N=1,d=4 supergravity solutions under
diffeormophisms and show that, in order to obtain consistent conditions
(``Killing equations'') invariant under local supersymmetry transformations,
one has to perform supersymmetry transformations generated by the superpartner
of the vector that generates standard diffeomorphisms, just as a superspace
analysis indicates. Using these transformations, we construct a Noether-Wald
charge of N=1,d=4 supergravity with fermionic contributions which is diff-
Lorentz- and supersymmetry-invariant (up to a total derivative).
