Shape matching with local descriptors is an underlyingscheme in shape analysis. We can visually confirm the matching results andalso assess them for shape classification. Generally, shape matching is im-plemented by determining the correspondence between shapes that are rep-resented by their respective sets of sampled points. Some matching meth-ods have already been proposed; the main difference between them lies intheir choice of matching cost function. This function measures the dissim-ilarity between the local distribution of sampled points around a focusingpoint of one shape and the local distribution of sampled points around areferring point of another shape. A local descriptor is used to describe thedistribution of sampled points around the point of the shape. In this paper,we propose an extended scheme for shape matching that can compensatefor errors in existing local descriptors. It is convenient for local descriptorsto adopt our scheme because it does not require the local descriptors to bemodified. The main idea of our scheme is to consider the correspondenceof neighboring sampled points to a focusing point when determining thecorrespondence of the focusing point. This is useful because it increasesthe chance of finding a suitable correspondence. However, considering thecorrespondence of neighboring points causes a problem regarding compu-tational feasibility, because there is a substantial increase in the numberof possible correspondences that need to be considered in shape match-ing. We solve this problem using a branch-and-bound algorithm, for effi-cient approximation. Using several shape datasets, we demonstrate that ourscheme yields a more suitable matching than the conventional scheme thatdoes not consider the correspondence of neighboring sampled points, eventhough our scheme requires only a small increase in execution time.