Large-scale numerical simulations of a system of inelastic, rough, hard spheres of volume fraction phi(s) = 0.565, which are initially distributed randomly in a Couette geometry, show clear evidence of the movement of the particles in directions transverse to the bulk motion, This behavior of the aforementioned system, which has been considered as a model for a granular fluid, is consistent with recent experimental observations [Hsiau and Hunt, J. Fluid Mech. 251, 299 (1993)]. Based on the results obtained, there are indications that a bounded rapid granular flow could be a diffusive system at volume fractions even higher than 0.56. This finding contradicts earlier computer experiments [Campbell, J. Fluid Mech. 348, 85 (1997)] which found a rapidly flowing granular material is a diffusive system except at large solids concentrations (i.e., phi(s) > 0.56).