Current methods of functional brain connectivity from resting-state fMRI data such as linear correlation have limitations, which result in connectivity maps affected by indirect connections and information loss. To address these problems, we propose to use a multivariate conditional mutual information (mvCMI) measure. mvCMI is a multivariate association method, which does not discard information and eliminates indirect connections. We tested mvCMI for single-subject fMRI-connectivity analysis in 10 healthy subjects. mvCMI was able to generate single-subject maps of functional connectivity showing mostly direct connections; mvCMI-based connectivity-maps were more closely related to diffusion-tensor-imaging-based structural connectivity-maps than linear-correlation-based connectivity-maps.