We present a method for the extraction of the skeletons of broken handwritten characters. The proposed algorithm is based on a comparison of the directional movement of every segment of a broken character, and on the connection between two points on different boundaries whose direction appears to be contrary. If a segment cannot be connected with another segment with an almost opposite direction, the direction of the segment will be turned at an angle until it connects with another segment. The application of the algorithm smoothes the character and removes small gaps and noise on its boundaries. The noniterative skeletonization process is based on the distances from character pixels to the boundaries. At the intersection, the algorithm will connect two thinned segments that are in a contrary direction and extend the segments that have no proper connecting points.