Although the covariances of electroencephalogram (EEG) signals are used in the classification of psychiatric diseases, the achieved performance is not still promising. Since schizophrenic and bipolar mood disorder (BMD) patients demonstrate similar signs and symptoms; distinguishing between them using qualitative criteria is hard. This study is aimed at classifying these patients by analyzing the manifold of their EEG signals' covariance. EEGs were recorded from 53 patients from both groups in the idle state. Each windowed signal is separately represented in manifold space and those frames which less deviated around the mean are chosen as the less affected noise frames. Nearest neighbor classifier is executed on the manifold space where each time the features of a patient is leaved out as the test case. The classification accuracy is highly improved up to 98.95% compared to the conventional methods. The achieved result is promising and the computational complexity is also suitable for real time processing.