Individual differences in brain metrics, especially connectivity measured with functional MRI, can correlate with differences in motion during data collection. The assumption has been that motion causes artifactual differences in brain connectivity that must and can be corrected. Here we propose that differences in brain connectivity can also represent a neurobiological trait that predisposes to differences in motion. We support this possibility with an analysis of intra- versus intersubject differences in connectivity comparing high- to low-motion subgroups. Intersubject analysis identified a correlate of head motion consisting of reduced distant functional connectivity primarily in the default network in individuals with high head motion. Similar connectivity differences were not found in analysis of intrasubject data. Instead, this correlate of head motion was a stable property in individuals across time. These findings suggest that motion-associated differences in brain connectivity cannot fully be attributed to motion artifacts but rather also reflect individual variability in functional organization.