Medial Axis (MA), also known as Centres of Maximal Disks, is a useful representation of a shape for image description and analysis. MA can be computed on a distance transform, where each point is labelled to its distance to the background. Recent algorithms allow one to compute Squared Euclidean Distance Transform (SEDT) in linear time in any dimension. While these algorithms provide exact measures, the only known method to characterise MA on SEDT, using local tests and Look-Up Tables (LUT), is limited to 2D and small distance values [Borgefors, et al., Seventh Scandinavian Conference on Image Analysis, 1991]. We have proposed [Remy, et al., Pat. Rec. Lett. 23 (2002) 649] an algorithm which computes the LUT and the neighbourhood to be tested in the case of chamfer distances. In this article, we adapt our algorithm for SEDT in arbitrary dimension and show that results have completely different properties.