This paper presents a new approach to functional magnetic resonance imaging (FMRI) data analysis. The main difference lies in the view of what comprises an observation. Here we treat the data from one scanning session (comprising t volumes, say) as one observation. This is contrary to the conventional way of looking at the data where each session is treated as t different observations. Thus instead of viewing the v voxels comprising the 3D volume of the brain as the variables, we suggest the usage of the vt hypervoxels comprising the 4D volume of the brain-over-session as the variables. A linear model is fitted to the 4D volumes originating from different sessions. Parameter estimation and hypothesis testing in this model can be performed with standard techniques. The hypothesis testing generates 4D statistical images (SIs) to which any relevant test statistic can be applied. In this paper we describe two test statistics, one voxel based and one cluster based, that can be used to test a range of hypotheses. There are several benefits in treating the data from each session as one observation, two of which are: (i) the temporal characteristics of the signal can be investigated without an explicit model for the blood oxygenation level dependent (BOLD) contrast response function, and (ii) the observations (sessions) can be assumed to be independent and hence inference on the 4D SI can be made by nonparametric or Monte Carlo methods. The suggested 4D approach is applied to FMRI data and is shown to accurately detect the expected signal