In generating a contour-parallel tool path, traditional offset methods usually offer an arc rounding option for superior sharp corners. For the inferior ones, however, they are left untreated. The inferior sharp corners are harmful to high-speed machining (HSM). They should be dealt with when they emerge for the first time; otherwise, they will be further inherited by the offset successors. In this paper, we presented a dual offset procedure to round the inferior sharp corners. For a given path, literally, the procedure conducts two offsets: at first, the path is offset inwards, generating an intermediate curve; then, this curve is further offset outwards, outputting the dual offset curve. The dual offset curve is guaranteed to be smooth. It is used to replace the original path. One side effect of this procedure is that many uncut regions will be left in the corner areas. These uncut regions are detected through a Boolean operation and removed by smooth clearup tool paths. Finally, the dual offset and clear-up tool paths are connected with a set of linking arcs. The proposed smooth tool path generation method is implemented and verified by several examples. Comparative cutting simulations show that this method has a potential to improve the machining efficiency in terms of HSM with nearly a zero cost.