A recurring issue in neuroscience concerns evidence as to whether two or more brain regions implement qualitatively different functions. Here we introduce the application of state-trace analysis to measures of neural activity, illustrating how this analysis can furnish compelling evidence for qualitatively different functions, even when the precise "neurometric" mapping between function and brain measure is unknown. In doing so, we address a long-standing debate about the brain systems supporting human memory: whether the hippocampus and the perirhinal cortex, two key components of the medial temporal lobe memory system, provide qualitatively different contributions to recognition memory. An alternative account has been that both regions support a single shared function, such as memory strength, with the apparent dissociations obtained by previous neuroimaging studies merely reflecting different, nonlinear neurometric mappings across regions. To adjudicate between these scenarios, we analyze intracranial electroencephalographic data obtained directly from human hippocampus and perirhinal cortex during a recognition paradigm and apply state-trace analysis to responses evoked by the retrieval cue as a function of different types of memory judgment. Assuming only that the neurometric mapping in each region is monotonic, any unidimensional theory (such as the memory-strength account) will produce a monotonic state trace. Critically, results showed a nonmonotonic state trace; that is, activity levels in the two regions did not show the same relative ordering across memory conditions. This nonmonotonic state trace demonstrates that there are at least two different functions implemented across the hippocampus and perirhinal cortex, allowing formal rejection of a single-process account of medial temporal lobe contributions to recognition memory.