  In this paper, a new locally supersymmetric two brane Randall-Sundrum model
is constructed. The construction starts from a D=5, N=2 gauged
Yang-Mills/Einstein/tensor supergravity theory with scalar manifold M = SO(1,1)
x SO(2,1) / SO(2) and gauge group U(1)_R x SO(2). Here, U(1)_R is a subgroup of
the R-symmetry group SU(2)_R and SO(2) is a subgroup of the isometry group of
M. Next, the U(1)_R gauge coupling g_R is replaced by g_R sgn(x^5) and the
fifth dimension is compactified on S^1 / Z_2. The conditions of local
supersymmetry for the bulk plus brane system admit a Randall-Sundrum vacuum
solution with constant scalars. This vacuum preserves N=2 supersymmetry in the
AdS_5 bulk and N=1 supersymmetry on the Minkowski 3-branes.
