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A novel approach for aligning multistation unregistered Light Detection and Ranging (LiDAR) point clouds is presented in this letter. It is designed to find the rigid rotations and translations between two data sets using hybrid conjugate features, including points, lines, planes, and groups of points. In addition, the proposed solution is expressed in a closed form, meaning that neither an initial alignment nor an iterative computation is required. Based on the numerical results from a real case study, it has been demonstrated that the proposed approach is capable of giving an efficient and reliable alignment solution. With the aforementioned advantages, the proposed technique can not only be directly implemented in a general analysis of LiDAR surveying data but will also particularly benefit those applications where classical point-based iterative analysis approaches are not practically feasible (e.g., an application without a sufficient number of connecting points).