Schizophrenia is associated with disconnectivity in the brain although it is still unclear whether changes within or between hemispheres are of greatest importance. In this paper, an analysis of 152 schizophrenia patients compared with 122 healthy controls was carried out. Comparisons were also made with 39 depression patients and 37 controls to examine whether brain-wide changes in inter- or intra-hemispheric functional connectivity are most associated with the disorder and can distinguish it from depression. The authors developed new techniques (first and second order symmetry) to investigate brain-wide changes in patients (45 regions per hemisphere) and their association with illness duration and symptom severity. Functional connectivity between the same regions in left- and right-hemispheres (first order symmetry) was significantly reduced as was that between the same pairs of regions in the left- and right-hemispheres (second order symmetry) or using all possible inter-hemispheric connections in schizophrenia patients. By contrast, no significant changes were found for brain-wide intra-hemispheric links. First order symmetry changes correlated significantly with positive and negative symptom severity for functional connections linked via the anterior commissure and negative symptoms for those linked via the corpus callosum. Support vector machine analysis revealed that inter-hemispheric symmetry changes had 73–81% accuracy in discriminating schizophrenia patients and either healthy controls or depressed patients. In conclusion, reduced brain-wide inter-hemispheric functional connectivity occurs in schizophrenia, is associated with symptom severity, and can discriminate schizophrenia patients from depressed ones or healthy controls. Brain-wide changes in inter-hemispheric connections may therefore provide a useful potential biomarker for schizophrenia.