In this paper, we study the 1-biconservative timelike hypersurfaces of the pseudo-Euclidean 5-space E^5_1. This research subject comes from the variational problem of the conservative stress-energy tensor associated to the biharmonic submanifolds. We show that every 1-biconservative Lorentz hypersurface of E^5_1 with constant mean curvature and at least three principal curvatures has constant scalar curvature.
