Skeletons are compact shape descriptions of discrete images. They have been extensively studied because of their utility in various applications such as data compression, shape abstraction, navigation and features detection. In this article, a new Euclidean skeletal definition for 2D discrete objects based on the Distance Map (DMAT) is being proposed. As a novel feature, it is shown that this skeleton is a connected subset of the discretization of the continuous medial axis of the object. Because of this property, the DMAT is 8-connected, it reflects all the features of the object and it preserves its topological characteristics. In addition, it provides dimensionality reduction, symmetry detection and invertibility. Moreover, it has a reasonable size and it guarantees low thickness.