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Deviations from body symmetry are theorized to indicate developmental instability, and have small associations with low socioeconomic status (SES). Previous studies have reported small negative associations between body asymmetry and cognitive functioning, but relationships between brain asymmetry and cognitive functioning remain unclear. The present study investigated the association between general intelligence (a latent factor derived from a factor analysis on 13 cognitive tests) and the asymmetry of four structural measures of brain hemispheric asymmetry: cortical surface area, cortical volume, cortical thickness, and white matter fractional anisotropy. The sample comprised members of the Lothian Birth Cohort 1936 (LBC1936, N = 636, mean age = 72.9 years). Two methods were used to calculate structural brain asymmetry: in the first method, regions contributed equally to the overall asymmetry score; in the second method, regions contributed proportionally to their size. When regions contributed equally, cortical thickness asymmetry was negatively associated with general intelligence (β = -.18, p < .001). There was no association between childhood SES and thickness asymmetry, suggesting that other mechanisms are involved in the intelligence-cortical asymmetry association. Asymmetry of regions identified by the parieto-frontal integration theory (P-FIT) was not more strongly associated with general intelligence than non-P-FIT asymmetry across all cortical metrics. When regions contributed proportionally, there were no associations between general intelligence and any of the asymmetry measures. The implications of these findings, and of different methods of calculating cortical hemispheric asymmetry, are discussed.