  An off-shell formulation is given for the ``supersymmetry in singular
spaces'' which has recently been developed in an on-shell formalism by
Bergshoeff, Kallosh and Van Proeyen using supersymmetry singlet `coupling
constant' field and 4-form multiplier field in five-dimensional space-time. We
present this formulation for a general supergravity-Yang-Mills-hypermultiplet
coupled system compactified on an orbifold $S^1/Z_2$. Relations between the
bulk cosmological constant and brane tensions of the boundary planes are
discussed.
