The resolution of the incompressible Navier-Stokes equations is tricky, and it is well known that one of the major issue is to compute a divergence free velocity. The non-conforming Crouzeix-Raviart finite element are convenient since they induce piecewise mass conservation and satisfy the inf-sup condition. However, spurious velocities may appear and damage the approximation. In this contribution, we propose a scheme that allows one to reduce the spurious velocities by discretizing the gradient of pressure with a symmetric MPFA scheme (finite volume MultiPoint Flux Approximation) [1, 2].