Abstract : A skeleton is a thin centered structure within an object, which describes its topology and its geometry. The medial surface is one of the most known and used skeleton formulation. As other formulations, it contains noise, which complexifies its structure with useless parts. The connectivity of a skeleton is then unpredictable due to these useless parts. It can be a problem to segment the skeleton into logical components for example. We present here a technique whose purpose is to identify and structure such skeletal noise. It only requires a skeleton as input, making this work independent from any skeletonization process used to obtain the skeleton. We show in this paper that we significantly reduce the skeletal noise and produce clean skeletons that still capture every aspects of a shape. Those clean skeletons have the same local topology as the input ones, but with a clearer connectivity.