This paper deals with the issue of watermarking 2D-vector data (point coordinates) which are used in Geographical Information Systems (GIS). The tolerance range of the coordinates is used to embed the information. As an embedding constraint no violation of the tolerance range at each point may occur. In the first step of our approach we lay a rectangular grid over the map, where the origin, the extension, and the subdivision of this grid is only known by the embedder. Based on a secret key we choose two disjunctive sets A and B of grid elements namely “patches.” Now these selected elements are further divided into smaller subareas or “subpatches.” In subpatches belonging to set A the distances of points to a reference line within each subpatch are decreased while the distances of subpatches of set B are unchanged. In the retrieving procedure we consider all subpatches belonging to the sets A and B and calculate for each of the two sets their sample variance. The decision whether the map is watermarked with a certain key or not is based on this feature and is made with the help of a hypothesis test. The proposed method is robust against attacks changing the coordinates within the tolerance range and against polygon simplification procedures.