Glaucoma is considered a progressive optic neuropathy because of the damage and death of the retinal ganglion cells. It is also a neurodegenerative disease because it affects neural structures in the visual system and beyond, including the corpus callosum–the largest white matter structure involved in inter-hemispheric transfer of information. In this study we probed the dysfunction of the inter-hemispheric processing in patients with mild glaucoma using the phenomenon of binocular rivalry. Patients with mild glaucoma and no measurable visual field defects and age-matched controls underwent a thorough visual assessment. Then they participated in a series of psychophysical tests designed to examine the binocular rivalry derived from intra- and inter-hemispheric processing. Static horizontal and vertical sinewave gratings were presented dichoptically using a double-mirror stereoscope in 3 locations: centrally, to probe inter-hemispheric processing, and peripherally to the left or to the right, to probe intra-hemispheric processing. Although the two groups were matched in functional measures, rivalry rate of the glaucoma group was significantly lower than that of the control group for the central location, but not for the peripheral location. These results were driven mainly by the patients with normal tension glaucoma whose average rivalry rate for the central location (from which information reaches the two hemispheres) was almost half (46% lower) that of the controls. These results indicate a dysfunction in inter-hemispheric transfer in mild glaucoma that can be detected behaviourally before any changes in standard functional measures.