We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite element method of degree one converges only in O(Öh) for the L2-norm of the vorticity. We propose to use harmonic functions to approach the vorticity along the boundary. Discrete harmonics are functions that are used in practice to derive a new numerical method. We prove that we obtain with this numerical scheme an error of order O(h) for the L2-norm of the vorticity.