Isosurface generation algorithms usually need a vertex-identification process since most of polygon-vertices of an isosurface are shared by several polygons. In our observation the identification process is often costly when traditional search algorithms are used. In this paper we propose a new isosurface generation algorithm that does not use the traditional search algorithm for polygon-vertex identification. When our algorithm constructs a polygon of an isosurface, it visits all cells adjacent to the vertices of the polygon, and registers the vertices to polygons inside the visited adjacent cells. The method does not require a costly vertex identification process, since a vertex is registered in all polygons that share the vertex at the same time, and the vertex is not required after the moment. In experimental tests, this method was about 20 percent faster than the conventional isosurface propagation method.