The goal of human brain mapping has long been to delineate the functional subunits in the brain and elucidate the functional role of each of these brain regions. Recent work has focused on whole-brain parcellation of functional Magnetic Resonance Imaging (fMRI) data to identify these subunits and create a functional atlas. Functional connectivity approaches to understand the brain at the network level require such an atlas to assess connections between parcels and extract network properties. While no single functional atlas has emerged as the dominant atlas to date, there remains an underlying assumption that such an atlas exists. Using fMRI data from a highly sampled subject as well as two independent replication data sets, we demonstrate that functional parcellations based on fMRI connectivity data reconfigure substantially and in a meaningful manner, according to brain state.