Independent component analysis (ICA), a data-driven approach utilizing high-order statistical moments to find maximally independent sources, has found fruitful application in functional magnetic resonance imaging (fMRI). A limitation of the standard fMRI ICA model is that a given component's time course is required to have the same delay at every voxel. As spatially varying delays (SVDs) may be found in fMRI data, using an ICA model with a fixed temporal delay for each source will have two implications. Larger SVDs can result in the splitting of regions with different delays into different components. Second, smaller SVDs can result in a biased ICA amplitude estimate due to only a slight delay difference. We propose a straightforward approach for incorporating this prior temporal information and removing the limitation of a fixed source delay by performing ICA on the amplitude spectrum of the original fMRI data (thus removing latency information). A latency map is then estimated for each component using the resulting component images and the raw data. We show that voxels with similar time courses, but different delays, are grouped into the same component. Additionally, when using traditional ICA, the amplitudes of motor areas are diminished due to systematic delay differences between visual and motor areas. The amplitudes are more accurately estimated when using a latency-insensitive ICA approach. The resulting time courses, the component maps, and the latency maps may prove useful as an addition to the collection of methods for fMRI data analysis.