We analyze the convergence of a substructuring iterative method with Lagrange multipliers , proposed recently by Farhat and Roux . The method decomposes finite element discretization of an elliptic boundary value problem into Neumann problems on the subdomains and a coarse problem for the subdomain nullspace components . For linear conforming elements and preconditioning by the Dirichlet problems on the subdomains , we prove the asymptotic bound on the condition number C(1 + log(H / h))(sup gamma ) , gamma = 2 or 3 , where h is the characteristic element size and H is the subdomain size .