Conventional kinesin walks by a hand-over-hand mechanism on the microtubule (MT) taking similar to 8 nm discrete steps and consumes one ATP molecule per step. The time needed to complete a single step is on the order of 20 mu s. We show, using simulations of a coarse-grained model of the complex containing the two motor heads, the MT and the coiled coil, that to obtain quantitative agreement with experiments for the stepping kinetics hydrodynamic interactions (HIs) have to be included. In simulations without hydrodynamic interactions, spanning nearly 20 mu s, not a single step was completed in one hundred trajectories. In sharp contrast, nearly 14% of the steps readied the target binding site within 6 mu s when HIs were included. Somewhat surprisingly, there are qualitative differences in the diffusion pathways in simulations with and without HI. The extent of movement of the trailing head of kinesin on the MT during the diffusion stage of stepping is considerably greater in simulations with HI than in those without HI. It is likely that inclusion of HI is crucial in the accurate description of motility of other motors as well.