Kinesin is a molecular walking machine that organizes cells by hauling packets of components directionally along microtubules. The physical mechanism that impels directional stepping is uncertain. We show here that, under very high backward loads, the intrinsic directional bias in kinesin stepping can be reversed such that the motor walks sustainedly backwards in a previously undescribed mode of ATP-dependent backward processivity. We find that both forward and backward 8-nm steps occur on the microsecond timescale and that both occur without mechanical substeps on this timescale. The data suggest an underlying mechanism in which, once ATP has bound to the microtubule-attached head, the other head undergoes a diffusional search for its next site, the outcome of which can be biased by an applied load.