While the fourth human visual field map (hV4) has been studied for two decades, there remain uncertainties about its spatial organization. In analyzing fMRI measurements designed to resolve these issues, we discovered a significant problem that afflicts measurements from ventral occipital cortex, and particularly measurements near hV4. In most hemispheres the fMRI hV4 data are contaminated by artifacts from the transverse sinus (TS). We created a model of the TS artifact and showed that the model predicts the locations of anomalous fMRI responses to simple large-field on-off stimuli. In many subjects, and particularly the left hemisphere, the TS artifact masks fMRI responses specifically in the region of cortex that distinguishes the two main hV4 models. By selecting subjects with a TS displaced from the lateral edge of hV4, we were able to see around the vein. In these subjects, the visual field coverage extends to the lower meridian, or nearly so, consistent with a model in which hV4 is located on the ventral surface and responds to signals throughout the full contralateral hemifield.