ATP synthase mediates proton flow through its membrane portion, F 0 , which drives the synthesis of ATP in its headpiece, F 1 . The F 1 -portion contains a hexagonal array of three subunits ␣ and three  encircling a central subunit ␥, that in turn interacts with a smaller and with F 0 . Recently we reported that the application of polarized absorption recovery after photobleaching showed the ATP-driven rotation of ␥ over at least two, if not three, . Here we extend probes of such rotation aided by a new theory for assessing continuous versus stepped, Brownian versus unidirectional molecular motion. The observed relaxation of the absorption anisotropy is fully compatible with a unidirectional and stepping rotation of ␥ over three equidistantly spaced angular positions in the hexagon formed by the alternating subunits ␣ and . The results strongly support a rotational catalysis with equal participation of all three catalytic sites. In addition we report a limited rotation of ␥ without added nucleotides, perhaps idling and of Brownian nature, that covers only a narrow angular domain.