Measurements of axial segregation of binary mixtures of glass beads having different diameters in a rotating horizontal cylinder are reported. For rotation speeds of ∼15 rpm a mixed state quickly (within a few minutes) segregates into sharp bands of alternating large and small glass beads along the axis of rotation. Decreasing the rotation speed to ∼5 rpm causes the bands to disappear, restoring the mixed state. The process is reversible upon increasing the rotation rate, though the exact location and width of the bands vary from run to run. The axial segregation phenomena are analyzed in terms of a diffusion equation where the effective diffusion coefficient is the difference between segregating drift and normal Fickian diffusion.