Renumbering algorithms commonly in use for the band solver are generally applicable for any kind of linear equations, and, therefore, we may say that they cann't effectively utilize the characteristics of the finite element mesh. In this paper we investigate the characteristics of the finite element mesh systems, and introduce them into Taniguchi-Shiraishi Algorithm which already introduced some properties of FEM mesh systems. And through several numerical experiments it is proved that this improved algorithm is one of the fastest one.