SUMMARYA complementary set of Reynolds-averaged Navier-Stokes (RANS) equations has been developed for steady incompressible, turbulent ows. The method is based on the Helmholtz decomposition of the velocity vector ÿeld into a viscous and a potential components. In the complementary RANS solver a potential solution coexists with a viscous solution with the purpose of contributing to a fastest decay of the viscous solution in the far ÿeld. The proposed complementary RANS equations have been validated for steady laminar and turbulent ows. The computational results show that the complementary RANS solver is able to produce less grid-dependent solutions than a conventional RANS solver.