We use the Kruskal time coordinate T to define the initial time. By this way, the stability study naturally becomes the one connected with the two regions, i.e. the white-hole-connected region and the black-hole-connected region.The union of the two regions covers the Schwarzschild space-time (r ≥ 2m). We also obtain the very reasonable conclusion: the white-hole-connected region is unstable and the black-hole-connected region is stable.