We set up a gauge finite element formulation of the 2D steady state incompressible Stokes problem. This formulation allows to decouple the two unknowns from the equations and to take account for the boundary conditions in a non-iterative way. A finite element discretization is used to obtain numerical convergence results. The method is then applied to the Navier-Stokes equations (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.