Cytoplasmic dynein is a homodimeric AAA+ motor that transports a multitude of cargos toward the microtubule minus end. How the two catalytic head domains interact and move relative to each other during processive movement is unclear. Here, we tracked the relative positions of both heads with nanometer precision and directly observed the heads moving independently along the microtubule. The heads remained widely separated, and their stepping behavior varied as a function of interhead separation. One active head was sufficient for processive movement, and an active head could drag an inactive partner head forward. Thus, dynein moves processively without interhead coordination, a mechanism fundamentally distinct from the hand-over-hand stepping of kinesin and myosin.