This note shows how the cubed-sphere grid can be extended (i.e., halo filling) to achieve high-order representation of fields and derivatives near the panel edges and specifically the corners of the cubed sphere. Thismakes it possible to obtain uniformly high-ordermulti-dimensional approximations and specifically makes the use of high-order finite differences/volumes or fully multi-dimensional semi-Lagrangian schemes viable options with the cubed sphere.