This paper presents an analysis for the variation of tool retraction length. Tool retraction, in zigzag pocket machining, is a non-productive operation in which the tool moves to any remaining regions for machining. Earlier, we developed an algorithm of generating tool retraction length in simple polygonal shapes. In the algorithm, we considered a reflex profile of cutting direction in a polygonal shape. Considering reflex profiles of cutting direction, the polygon is decomposed to subregions, triangles and quadrilaterals, which do not need any tool retraction. Consequently, we propose a new result that the shortest length of tool retraction presents a cutting direction parallel to concave edges. Examples are shown to verify the validity.