Studies of immobilized kinesin have shown that a single dimeric molecule can maintain contact with and drive sliding of a microtubule. In solution, however, native kinesin binds microtubules too weakly and hydrolyses ATP too slowly to produce the high sliding velocities seen in motility assay. This apparent inhibition in solution appears to be caused by the binding of kinesin's tail domains to its motor (head) domains in a folded conformation. DKH392, a construct containing two heads but no tails, has been shown to display both tight binding to microtubules and high ATPase rates. Furthermore, it retains one molecule of ADP per dimer when bound to microtubules, which could facilitate a 'hand-over-hand' mechanism for processive motion. Here we show that DKH392 hydrolyses more than 100 ATP molecules per diffusional encounter with a microtubule, even in the high-salt conditions encountered physiologically. This provides direct evidence that kinesin's activity is highly processive, with the motor remaining attached to a microtubule through many cycles of ATP hydrolysis.