  It is shown that the supersymmetric extension of the Stelle-West formalism
permits the construction of an action for $(3+1)$-dimensional N=1 supergravity
with cosmological constant genuinely invariant under the $OSp(4/1).$ Since the
action is invariant under the supersymmetric extension of the $AdS$ group, the
supersymmetry algebra closes off shell without the need for auxiliary fields.
The limit case $m\to 0$, i.e.$(3+1)$ -dimensional N=1 supergravity invariant
under the Poincar\'{e} supergroup is also discussed.
