Water diffusion is extremely anisotropic in brain white matter, depending on myelin fiber orientation. A suggested, but unproven cause of anisotropy is that, in the direction transverse to the myelin fibers, axonal water diffusion is prevented by the presence of the myelin sheath. We found, however, using an ultra-fast nuclear magnetic resonance imaging technique, that the dependence of the diffusion coefficient on the diffusion time does not support the model of water restriction by impenetrable barriers. These results, which were obtained non-invasively in vivo in the human brain, imply that water diffuses with a measurable rate across myelin fibers.