The numerical simulation of two-phase flow in a porous medium may lead, when using coupled finite volume schemes on structured grids, to the apparition of the so-called Grid Orientation Effect (GOE). We propose in this paper a procedure to eliminate this phenomenon, based on the use of new fluxes with a new stencil in the discrete version of the convection equation, without changing the discrete scheme for computing the pressure field. Numerical results show that the GOE does not significantly decrease with the size of the discretization using the initial scheme on the coupled problem, but that it is efficiently suppressed by the new procedure, even on coarse meshes. A mathematical study, based on a weak BV inequality using the new fluxes, confirms the convergence of the modified scheme in a particular case.