In mathematical physics, the stable hypersurfaces of constant mean curvature in pseudo-Euclidian spheres have been interested by many researchers on general relativity. As an extension, the notion of index of stability has been introduced for unstable ones. The stability index (as a rate of distance from being stable) is defined n terms of the Laplace operator Delta as the trace of Hessian tensor. In this paper, we study an extension of stability index (namely, 1-index) of hypersurfaces with constant scalar curvature in pseudo-Euclidian sphere S_1^{n+1}. 1-index is defined based on the Cheng-Yau operator \Box as a natural extension of \Delta.
