In robotic applications, many pose problems involve solving the homogeneous transformation based on the special Euclidean group SE(n) . However, due to the nonconvexity of SE(n) , many of these solvers treat rotation and translation separately, and the computational efficiency is still unsatisfactory. A new technique called the SE(n)++ is proposed in this article that exploits a novel mapping from SE(n) to SO(n + 1) . The mapping transforms the coupling between rotation and translation into a unified formulation on the Lie group and gives better analytical results and computational performances. Specifically, three major pose problems are considered in this article, that is, the point-cloud registration, the hand-eye calibration, and the SE(n) synchronization. Experimental validations have confirmed the effectiveness of the proposed SE(n)++ method in open datasets.