  Straightforward application of the standard Noether method in supergravity
theories yields an incorrect superpotential for local supersymmetry
transformations, which gives only half of the correct supercharge. We show how
to derive the correct superpotential through Lagrangian methods, by applying a
criterion proposed recently by one of us. We verify the equivalence with the
Hamiltonian formalism. It is also indicated why the first-order and
second-order formalisms lead to the same superpotential. We rederive in
particular the central extension by the magnetic charge of the ${\cal N}_4 =2$
algebra of SUGRA asymptotic charges.
