We present IRAv3, which is built upon the state-of-the-art rotation averaging method, IRA++, to push this fundamental task in 3D computer vision one step further. The key observation of this letter lies in that during IRA++, the community detection-based Epipolar-geometry Graph (EG) clustering is preemptive and permanent, which is not relevant to the follow-up rotation averaging task and limits the upper bound of absolute rotation estimation accuracy. In this letter, however, the EG clustering is performed along with the cluster-wise absolute rotation estimation, i.e. instead of pre-determination, the affiliation of each vertex to which EG cluster is determined “on the fly”, and the EG clustering finishes until all the vertices find the clusters they belong to, together with their absolute rotations estimated (in the local coordinate systems of the clusters they attached). By this way, a rotation averaging-targeted and -friendly EG clustering is obtained, which facilitates the rotation averaging task in turn. Experiments on both 1DSfM and KITTI odometry datasets demonstrate the effectiveness of our proposed IRAv3 on large-scale rotation averaging problems and its advantages over its previous works (IRA and IRA++) and other state of the arts.