There are plenty of different algorithms for aligning pairs of 2D-shapes and point-sets. They mainly concern the establishment of correspon-dences and the detection of outliers. All of them assume that the aligned shapes are quite similar and belonging to the same class of shapes. But special problems arise if we have to align shapes that are very different, for example aligning concave shapes to convex ones. In such cases it is indispensable to take into account the order of the point-sets and to enforce legal sets of correspondences; otherwise the calculated distances are incorrect. We present our novel shape alignment algorithm which can handle such cases also. The algorithm establishes legal one-to-one point correspondences between arbitrary shapes, represented as ordered sets of 2D-points and returns a distance measure which runs between 0 and 1.