Measures of cortical folding ('gyrification') and connectivity are both reported to be disrupted in schizophrenia. There are also reports that increases in prefrontal gyrification may be predictive of subsequent illness in individuals at familial risk of the disorder. Such measures therefore have important potential clinical relevance. The nature of the relationship between cortical morphology and underlying connectivity is however unclear. In the current study we sought to explore the relationship between measures of gyrification and functional connectivity in a cohort of individuals at high genetic risk for the disorder. The theoretical background is based on the hypothesis that increased gyrification index (GI) in the prefrontal cortex may reflect increased short range regional connectivity. The cohort comprised 68 young unaffected relatives of schizophrenia patients and 21 healthy controls. Cortical folding was assessed using an automated Gyrification Index method (A-GI). Participants performed the Hayling sentence completion paradigm in the scanner and measures of functional connectivity were assessed using a correlation based approach. In the high risk subjects significant positive associations were found between prefrontal GI and prefrontal lateral-medial connectivity, while a negative correlation was found between prefrontal GI and prefrontal-thalamic connectivity. These associations indicate that measures describing morphological features of the brain surface relate to measures of underlying functional connectivity in the high risk subjects. Correlations in high risk people were more pronounced than in control subjects. We suggest our previous finding of increased prefrontal gyrification may therefore relate to increased local short range prefrontal connectivity and reduced long range connectivity.