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(2, 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. (c) 2006 Elsevier B.V. All rights reserved.