Schizophrenia (SZ) and bipolar disorder (BP) are currently diagnosed on the basis of a constellation of psychiatric symptoms and longitudinal course. The clinical profile of SZ and BP can sometimes look similar, especially when symptoms are overlapping. The determination of a reliable biologically-based indicator of these diseases (a biomarker) would be a significant advance and could provide the groundwork for developing more rigorous tools for differential diagnosis and assignment of treatments. Recently, independent component analysis applied to functional magnetic resonance imaging (fMRI) data has been fruitful in grouping the data into meaningful spatially independent components. We propose an automated way to identify two distinct brain networks or 'modes' which occur in regions implicated in schizophrenia. Following identification, we propose a method for combining two brain modes and develop a supervised classification algorithm for discriminating subjects with bipolar disorder, chronic schizophrenia, and healthy controls. An adaptive threshold applied to pair-wise mean difference images for the two spatial modes is trained to minimize the total error based upon the Euclidean distance between the group mean images and the images to be classified. Using a fully validated leave-one-out approach, results indicate an average sensitivity and specificity of 90% and 95%, respectively. In summary, we show that using features derived from fMRI data with ICA and a supervised classification approach, we can objectively separate diagnostic groups and suggests that combining multiple brain networks may improve our ability to distinguish diseases processes.