The analysis of single trials of an fMRI experiment is difficult because the BOLD response has a poor signal to noise ratio and is sometimes even inconsistent across trials. We propose to use non-negative matrix factorization (NMF) as a new technique for analyzing single trials. NMF yields a matrix decomposition that is useful in this context because it elicits the intrinsic structure of the single-trial data. The results of the NMF analysis are then processed further using clustering techniques. In addition to analyzing single trials in one brain region, the method is also suitable for investigating interdependencies between trials across brain regions. The method even allows to analyze the effect that a trial has on a subsequent trial in a different region at a significant temporal offset. This distinguishes the present method from other methods that require interdependencies between brain regions to occur nearly simultaneously. The method was applied to fMRI data and found to be a viable technique that may be superior to other matrix decomposition methods for this particular problem domain.