Abstract: We prove that, in the Minkowski space, if a spacelike, (n – 1)-convex hypersurface M of constant $\sigma_{n-1}$ curvature has bounded principal curvatures, then M is convex. Moreover, if M is not strictly convex, after an $R^{n,1}$ rigid motion, M splits as a product $M^{n-1} \times R.$ We also construct nontrivial examples of strictly convex, spacelike hypersurface M with constant $\sigma_{n-1}$ curvature and bounded principal curvatures. This is a joint work with Changyu Ren and Zhizhang Wang.