Schizophrenia is considered a disorder of abnormal brain connectivity. Although whole brain maps of averaged bivariate voxel correlations have been successfully applied to study connectivity abnormalities in schizophrenia these maps do not adequately explore the multivariate nature of brain connectivity. Here we adapt a novel method for high-dimensional regression (supervised principal component regression) to estimate brain maps of multivariate non redundant connectivity (NRC) from resting functional Magnetic Resonance Imaging (fMRI) data of 116 patients with schizophrenia and 122 matched controls. Disorder related differences in NRC involved caudate hyper-connectivity and hypo-connectivity of several cortical areas such as the dorsal cingulate, the cuneus and the right postcentral cortex. These abnormalities were coupled with abnormalities in the amplitude of signal fluctuations and, to a minor extent, with differences in the dimensionality of connectivity patterns as quantified by the number of supervised principal components. Second level seed correlation analyses linked the observed abnormalities to an additional set of brain regions relevant to schizophrenia such as the thalamus and the temporal cortex. The non redundant connectivity maps proposed here are a new tool that will complement the information provided by other already available voxel based whole brain connectivity measures.