It is presented in this study a new efficient intelligent machining strategy, which can be used to remove the uncut volume at the boundary region of curved surfaces caused by cutter interference. The geometric form definitions and recognition of topological features of the surface triangulation mesh are used to generate cutter paths along successive and interconnected steepest pathways, that minimize the cusp height left after flat end milling. In order to machine the uncut volume gradually, the z-map cutter centers are adjusted to avoid cutter interference for the 6 kinds of avoidance types. And then, the generative subsequent paths are sequenced to determine the second step cutter paths for the next uncut volume. For the 2 kinds of test models with convex and concave surface region, the implemented software algorithm is evaluated by investigating the residual swelling of uncut volume for each machining step.