Honeybees remember the shapes of flowers and are guided by visual landmarks on their foraging trips. How insects recognize visual patterns is poorly understood. Experiments suggest that they try to match retinotopically the incoming visual pattern with a previously stored memory image. But bees can be conditioned to individual pattern parameters such as orientation of contours, colour or size. These and other results are difficult to reconcile with simple template matching. In such investigations, freely moving animals are observed; their behaviour and visual input, therefore, are not well known. Mostly, processing strategies are inferred from stimulus design. We have studied visual pattern recognition with tethered flies (Drosophila melanogaster) in a flight simulator and report here that flies store visual images at, or together with, fixed retinal positions and can retrieve them from there only. Position invariance, an acknowledged property of human pattern recognition, may not exist as a primary mechanism in insects.