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As an essential part of structure from motion (SfM) and Simultaneous Localization and Mapping (SLAM) systems, motion averaging has been extensively studied in the past years and continues to attract surging research attention. While canonical approaches such as bundle adjustment are predominantly inherited in most of state-of-the-art SLAM systems to estimate and update the trajectory in the robot navigation, the practical implementation of bundle adjustment in SLAM systems is intrinsically limited by the high computational complexity, unreliable convergence and strict requirements of ideal initializations. In this paper, we lift these limitations and propose a novel optimization backbone for visual SLAM systems, where we leverage rotation averaging to improve the accuracy, efficiency and robustness of conventional monocular SLAM pipelines. In our approach, we first decouple the rotational and translational parameters in the camera rigid body transformation and convert the high-dimensional non-convex nonlinear problem into tractable linear subproblems in lower dimensions, and show that the subproblems can be solved independently with proper constraints. We apply the scale parameter with $l_1$-norm in the pose-graph optimization to address the rotation averaging robustness against outliers. We further validate the global optimality of our proposed approach, revisit and address the initialization schemes, pure rotational scene handling and outlier treatments. We demonstrate that our approach can exhibit up to 10x faster speed with comparable accuracy against the state of the art on public benchmarks.