At the heart of feature integration theory is a master map which operates on dimension-based feature maps. It is assumed that these feature maps are organized retinotopically. If in conjunction search, for example, a horizontal green line has to be searched for, the master map 'looks' at the retinotopic position (x,y) in both the color and the orientation maps whether they contain a 'green' and a 'horizontal' entry, respectively. Here, we show evidence that attention operates on non-retinotopically organized feature maps. We presented a Ternus - Pikler display where three squares shifted horizontally back and forth by one inter-square distance. This created a periodic motion where two squares always overlapped in successive frames. Each square contained a different conjunction search display and the observers were asked to identify a conjunction target in the central square. Theories assuming retinotopically organized feature maps predict poor performance because of the spatial overlap of the different search displays in successive frames. However, we found a remarkably good performance. Moreover, observers clearly perceived the search display in the central square because, as we argue, perception and attention are based on non-retinotopic feature maps--contrary to most theories of visual search.