Myosin VI (MVI) is the only known member of the myosin superfamily that, upon dimerization, walks processively towards the pointed end of the actin filament. The leading head of the dimer directs the trailing head forward with a power stroke, a conformational change of the motor domain exaggerated by the lever arm. Using a new coarse-grained model for the power stroke of a single MVI, we provide the molecular basis for its motility. We show that the power stroke occurs in two major steps: first, the motor domain attains the post-stroke conformation without directing the lever arm forward; second, the lever arm reaches the post-stroke orientation by undergoing a rotational diffusion. From the analysis of the trajectories, we discover that the potential that directs the rotating lever arm towards the post-stroke conformation is almost flat, implying that the lever arm rotation is mostly uncoupled from the motor domain. Because a backward load comparable with the largest inter-head tension in a MVI dimer prevents the rotation of the lever arm, our model suggests that the leading-head lever arm of a MVI dimer is uncoupled, in accord with the inference drawn from polarized Total Internal Reflection Fluorescence (polTIRF) experiments. Our simulations are in quantitative agreement with polTIRF experiments, which validates our structural insights. Finally, we discuss the implications of our model in explaining the broad step-size distribution of MVI stepping pattern, and we make testable predictions.