The effects of fluctuations and noise in the interplanetary magnetic field and in the cosmic ray flux on the diffusive streaming direction obtained from the neutron monitor diurnal anisotropy are presented. Cosmic rays are assumed to stream along the instantaneous magnetic field, but the average diurnal flux still differs from the daily average field direction owing to averaging effects and noise. Comparisons with observational data are given, and the results indicate the existence of a daily non-field-aligned anisotropy about one fourth as large as the field-aligned anisotropy. It is suggested that this anisotropy is due to cosmic ray streaming caused by the antisymmetric terms in the diffusion tensor.