A multivariate non-parametric approach for the processing of fMRI group data is important to address variability of hemodynamic responses across subjects, sessions, and brain regions. Independent component analysis (ICA) has a limitation during the inference of group effects due to a permutation problem of independent components. In order to address this limitation, we present an independent vector analysis (IVA) for the processing of fMRI group data. Compared to the ICA, the IVA offers an extra dimension for the dependent parameters, which can be assigned for the automated grouping of dependent activation patterns across subjects. The IVA was applied to the fMRI data obtained from 12 subjects performing a left-hand motor task. In comparison with conventional univariate methods, IVA successfully characterized the group-representative activation time courses (as component vectors) without extra data processing schemes to circumvent the permutation problem, while effectively detecting the areas with hemodynamic responses deviating from canonical, model-driven ones.