In recent years, a nonoverlapping domain decomposition iterative procedure, which is based on using Robin-type boundary conditions as information transmission conditions on the subdomain interfaces, has been developed and analyzed. The idea of employing Robin-type boundary conditions as interface conditions was first proposed by P.L. Lions. It is known that the convergence rate of this method is 1-O(h), where h is mesh size. In this talk, the convergence rate will be improved to 1 - O(h^1/2 H^-1/2) by choosing suitable parameter on the interfaces, where H is the subdomain size. Counter examples will be constructed to show that the convergence rate is sharp.