Inferring interactions between discrete brain regions has being increasingly recognized as important for studying brain in both normal and disease states. In addition to static brain network inference, the temporal dynamics of brain connectivity access the brain in the temporal dimension and provide a new perspective to the understanding of brain function. Most current brain network modeling approaches are based on assumptions that brain connections are purely static or purely dynamic. This may be unrealistic as the brain must strike a balance between stability and flexibility. In this paper, we propose making joint inference of time invariant connections and time varying coupling patterns by employing a multitask learning model followed by a least square approach to precisely estimate the connectivity coefficients. When applied to a real resting state fMRI study, the eigenconnectivity networks were extracted to obtain the representative patterns of both static and dynamic brain connectivity networks. The results demonstrated that the static and dynamic connectivity networks may represent complementary information on the brain connectivity patterns.