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Covariance-based methods of exploration of functional connectivity of the brain from functional magnetic resonance imaging (fMRI) experiments, such as principal component analysis (PCA) and structural equation modeling (SEM), require a priori knowledge such as an anatomical model to infer functional connectivity. In this research, a hybrid method, combining independent component analysis (ICA) and SEM, which is capable of deriving functional connectivity in an exploratory manner without the need of a prior model is introduced. The spatial ICA (SICA) derives independent neural systems or sources involved in task-related brain activation, while an automated method based on the SEM finds the structure of the connectivity among the elements in independent neural systems. Unlike second-order approaches used in earlier studies, the task-related neural systems derived from the ICA provide brain connectivity in the complete statistical sense. The use and efficacy of this approach is illustrated on two fMRI datasets obtained from a visual task and a language reading task.