The current Kinect system extracts human skeletons from depth images by supervised learning methods, which require a large number of marker-based motion capture data for training. However, with limited budget, motion capture devices are not available and motion capture data is difficult to collect. In this paper, we propose a unsupervised skeletonization method to extract human skeletons from depth images without any training data. It considers the symmetry of skeletons to object boundary. The boundaries of human body are first formed from the edges involved from the characteristic changes in depth, then boundary analysis is performed to identify boundaries with different types, next a two-step skeletonization scheme is adopted to compute skeletons from different types of boundaries separately, finally skeletons generated from the two steps are combined as the output. Experimental results show that without any markers for training, human skeletons obtained by the proposed method can represent both the body parts without occlusion and the main torso under occlusion.