A numerical algorithm for an external Dirichlet problem of the Poisson equation is considered. The domain O extending to infinity is divided into a bounded subdomain O0and the unbounded subdomain O1. The finite and the boundary element methods are applied to the boundary value problems in the bounded and the unbounded subdomains, respectively. An iterative scheme using the Dirichlet‐Neumann map on the interface ?O1is presented. The convergence of the scheme is mathematically guaranteed. A simple numerical example shows the effectiveness of our scheme.