False memories commonly activate the anterior/dorsolateral prefrontal cortex (A/DLPFC) and the hippocampus. These regions are assumed to work in concert during false memories, which would predict a positive correlation between the magnitudes of activity in these regions across participants. However, the A/DLPFC may also inhibit the hippocampus, which would predict a negative correlation between the magnitudes of activity in these regions. In the present functional magnetic resonance imaging (fMRI) study, during encoding, participants viewed abstract shapes in the left or right visual field. During retrieval, participants classified each old shape as previously in the left or right visual field followed by an unsure-sure-very sure confidence rating. The contrast of left-hits and left-misses produced two activations in the hippocampus and three activations in the left A/DLPFC. For each participant, activity associated with false memories (right-left-very sure responses) from the two hippocampal regions was plotted as a function of activity in each A/DLPFC region. Across participants, for one region in the left anterior prefrontal cortex, there was a negative correlation between the magnitudes of activity in this region and the hippocampus. This suggests that the anterior prefrontal cortex might inhibit the hippocampus during false memories and that participants engage either the anterior prefrontal cortex or the hippocampus during false memories.