  We propose a simple modification of standard WENO finite volume methods for
Cartesian grids, which retains the full spatial order of accuracy of the
one-dimensional discretization when applied to nonlinear multidimensional
systems of conservation laws.
  We derive formulas, which allow us to compute high-order accurate point
values of the conserved quantities at grid cell interfaces. Using those point
values, we can compute a high-order flux at the center of a grid cell
interface. Finally, we use those point values to compute high-order accurate
averaged fluxes at cell interfaces as needed by a finite volume method.
  The method is described in detail for the two-dimensional Euler equations of
gas dynamics. An extension to the three-dimensional case as well as to other
nonlinear systems of conservation laws in divergence form is straightforward.
Furthermore, similar ideas can be used to improve the accuracy of WENO type
methods for hyperbolic systems which are not in divergence form.
  Several test computations confirm the high-order accuracy for smooth
nonlinear problems.
