In selecting appropriate behaviors, animals should weigh sensory evidence both for and against specific beliefs about the world. For instance, animals measure optic flow to estimate and control their own rotation. However, existing models of flow detection can confuse the movement of external objects with genuine self motion. Here, we show that stationary patterns on the retina, which constitute negative evidence against self rotation, are used by the fruit fly Drosophila to suppress inappropriate stabilizing rotational behavior. In silico experiments show that artificial neural networks optimized to distinguish self and world motion similarly detect stationarity and incorporate negative evidence. Employing neural measurements and genetic manipulations, we identified components of the circuitry for stationary pattern detection, which runs parallel to the fly's motion- and optic flow-detectors. Our results exemplify how the compact brain of the fly incorporates negative evidence to improve heading stability, exploiting geometrical constraints of the visual world.