  We explore the supersymmetry invariance of a supergravity theory in the
presence of a non-trivial boundary. The explicit construction of a bulk
Lagrangian based on an enlarged superalgebra, known as $AdS$-Lorentz, is
presented. Using a geometric approach we show that the supersymmetric extension
of a Gauss-Bonnet like gravity is required in order to restore the
supersymmetry invariance of the theory.
