Abstract: The paper aims to present a method to maintain the neighboring relations before a point is moved without reconstructing the delaunay triangulation or the Voronoi diagram. A new concept of the Topology Stable Area is put forward firstly, then the two conditions which the point in the topology stable area should be met are proved by the empty circle rule of the delaunay triangulation, one is that the neighboring relations between the moving point and it’s first order neighboring point must be maintained, another is that there is no new first order neighboring point of the moving point is created. A novel calculation method of the topology stable area of the plane discrete points based on the Voronoi diagram and delaunay triangulation is presented. And it’s correctness is proved by the experiment.