N-sided hole filling plays an important role in vertex blending. To deal with the case that the corner is surrounded by rational surfaces (i.e. NURBS surfaces), an algorithm to fill n-sided holes with ɛ-G1 continuous NURBS patches that interpolate the given boundary curves and approximate the given cross-boundary derivatives is presented based on Piegl's method. The NURBS surfaces joining along inner or boundary curves have normal vectors that do not deviate more than the user-specified angular tolerance ɛ. The boundaries as well as cross-boundary derivatives can all be NURBS curves. No restrictions are imposed on the number of boundary curves, and the cross-boundary derivatives can be specified independently.