Detecting aligned 3D keypoints is essential under many scenarios such as object tracking, shape retrieval and robotics. However, it is generally hard to prepare a high-quality dataset for all types of objects due to the ambiguity of keypoint itself. Meanwhile, current unsupervised detectors are unable to generate aligned keypoints with good coverage. In this paper, we propose an unsupervised aligned keypoint detector, Skeleton Merger, which utilizes skeletons to reconstruct objects. It is based on an Autoencoder architecture. The encoder proposes keypoints and predicts activation strengths of edges between keypoints. The decoder performs uniform sampling on the skeleton and refines it into small point clouds with pointwise offsets. Then the activation strengths are applied and the sub-clouds are merged. Composite Chamfer Distance (CCD) is proposed as a distance between the input point cloud and the reconstruction composed of sub-clouds masked by activation strengths. We demonstrate that Skeleton Merger is capable of detecting semantically-rich salient keypoints with good alignment, and shows comparable performance to supervised methods on the KeypointNet dataset. It is also shown that the detector is robust to noise and subsampling. Our code is available at https://github.com/eliphatfs/SkeletonMerger.