  In this paper we consider the problem of spontaneous supersymmetry breaking
in $N=4$ supergravity interacting with vector multiplets. We start with the
ordinary version of such model with the scalar field geometry
$SU(1,1)/U(1)\otimes SO(6,m)/SO(6)\otimes SO(m)$. Then we construct a dual
version of this theory with the same scalar field geometry, which corresponds
to the interaction of arbitrary number of vector multiplets with the hidden
sector, admitting spontaneous supersymmetry breaking without a cosmological
term. We show that supersymmetry breaking is still possible in the presence of
matter fields.
