In the framework of on-line handwriting recognition, description methods based on detecting the elementary parts the ink can be decomposed into have been widely used. In the universe of Latin characters and Arabic numerals, straight segments and arcs of circle seems to have enough descriptive power to be assumed as elementary shapes. Under this assumption, the process of decomposing a word into elementary parts or strokes can be reformulated as a curve fitting problem where segments and arcs of circle are the primitives to fit within the original curve. The strokes provided by curve fitting algorithms, however, generally exhibit a very large variability in case of on-line handwriting, due to the occurrence of noisy writing speed variations along the ink, which produce both changes in the density of the points and local distortions. In this paper we propose a new decomposition method based on a multi-scale representation of the electronic ink. At each level, by using a suitable arclenght representation, points corresponding to curvature variations are recorded. These representations are then used to identify the points of the ink in which significant curvature variations occur at varying levels of detail: such points are considered as possible junctions between successive strokes. Preliminary experiments have shown that the method correctly decomposes the ink in the large majority of the cases. They also show that the method provides only a few, slightly different decompositions.