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The skeleton of a digital figure can often be regarded as a convenient alternative to the figure itself. It is useful both to diminish drastically the amount of data to be handled, and to simplify the computational procedures required for description and classification purposes. Thinning a digital figure down to its skeleton is a time-consuming process when conventional sequential computers are employed. The procedure we propose allows one to speed up the thinning transformation, and to get a well-shaped skeleton. After cleaning of the input picture has been performed, the pixels of the figure are labeled according to their distance from the background, and a set, whose pixels are symmetrically placed with respect to distinct contour parts of the figure, is found. This set is then given a linear structure by applying topology preserving removal operations. Finally, a pruning step, regarding branches not relevant in the framework of the problem domain, completes the process. The resulting skeleton is a labeled set of pixels which is shown to possess all the required properties, particularly those concerning connectedness, topology, and shape. Moreover, the original figure can almost completely be recovered by means of a reverse distance transformation. Only a fixed and small number of sequential passes through the picture is necessary to achieve the goal. The computational effort is rather modest, and the use of the proposed algorithm turns out to be more advantageous the greater the width of the figure to be thinned.