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A good motion model is a prerequisite for many approaches to simultaneous localization and mapping. Without an absolute reference, it is however difficult to prevent drift when estimating motion. To prevent orientation drift, our approach exploits typical features of indoor environments: Straight walls that are parallel or orthogonal to each other. Our idea is to detect walls in monocular depth measurements and to correct odometry obtained from matching successive images and from inertial measurements, such that the observed walls are aligned with the main orientation estimated from the map that is being built. The experimental results indicate that orientation drift can be prevented and orientation uncertainty can be reduced greatly when applying the proposed orthogonal wall correction. This can make the difference between reliable mapping and failure.