An original approach of the singular complement method for Maxwell's equations in bounded polygonal domains is presented. A splitting of the electric field à la Moussaoui is proposed: E=ER+λxP, where ER∈H1(ω)², λ depends on the data and domain and xP is known explicitly. The same splitting can used for the magnetic field. No cut-off function is needed and improved error estimates are derived. © 2004 Académie des sciences. Publié par Elsevier SAS. Tous droits réservés.