We present a new central scheme for approximating solutions of two-dimensional systems of hyperbolic conservation laws. This method is based on a modification of the staggered grid proposed in [jiang-tadmor] which prevents the crossings of discontinuities in the normal direction, while retaining the simplicity of the central framework. Our method satisfies a local maximum principle which is based on a more compact stencil. Unlike the previous method, it enables a natural extension to adaptive methods on structured grids.