In the visual cortex of higher mammals, neurons are arranged across the cortical surface in an orderly map of preferred stimulus orientations. This map contains 'orientation pinwheels', structures that are arranged like the spokes of a wheel such that orientation changes continuously around a centre. Conventional optical imaging first demonstrated these pinwheels, but the technique lacked the spatial resolution to determine the response properties and arrangement of cells near pinwheel centres. Electrophysiological recordings later demonstrated sharply selective neurons near pinwheel centres, but it remained unclear whether they were arranged randomly or in an orderly fashion. Here we use two-photon calcium imaging in vivo to determine the microstructure of pinwheel centres in cat visual cortex with single-cell resolution. We find that pinwheel centres are highly ordered: neurons selective to different orientations are clearly segregated even in the very centre. Thus, pinwheel centres truly represent singularities in the cortical map. This highly ordered arrangement at the level of single cells suggests great precision in the development of cortical circuits underlying orientation selectivity.