Functional MRI (fMRI) captures brain function by recording the oxygen consumption of a large number of brain voxels simultaneously along time. The set of time series obtained is typically decomposed using Principal Component Analysis (PCA) or Independent Component Analysis (ICA) to reveal the regions and networks organizing the brain. In this work, we introduce a novel decomposition approach. We separate brain activations and de-activation, and we separately decompose co-activations, captured by the correlation between the activations, co-deactivations measured by the correlation between the de-activations, and the correlations between activations and de-activations. The decomposition is performed by a nonnegative factorization method known to generate sparse decompositions, which we accelerate by extrapolation. As a result, our approach produces in reasonable time compact fMRI scans decompositions offering a rich interpretation of the interactions between brain regions. The experiments presented here, performed on a dataset of forty scans provided by the Human Connectome Project, demonstrate the quality of our decompositions and indicate that a speedup of an order of magnitude is offered by the extrapolation.