  Cosmic ray propagation is diffusive because of pitch angle scattering by
waves. We demonstrate that if the high-amplitude magnetohydrodynamic turbulence
with $\tilde B/\langle B\rangle \sim 1$ is present on top of the mean field
gradient, the diffusion becomes asymmetric. As an example, we consider the
vertical transport of cosmic rays in our Galaxy propagating away from a
point-like source. We solve this diffusion problem analytically using a
one-dimensional Markov chain analysis. We obtained that the cosmic ray density
markedly differs from the standard diffusion prediction and has a sizable
effect on their distribution throughout the galaxy. The equation for the
continuous limit is also derived, which shows limitations of the
convection-diffusion equation.
