Performance of patients with quadrant lesions on the inherently ambiguous Cognitive Bias Task (CBT) suggests sexual dimorphism in the fundamental aspects of functional cortical geometry, by emphasizing different cerebral axes. In right-handed males, extreme context-dependent and context-independent response selection biases are reciprocally linked to left vs. right frontal systems. In right-handed females, these complementary biases appear to be reciprocally linked to posterior vs. frontal cortices. Frontal lobe functions are more lateralized in males than females due to sexual dimorphism of the left frontal systems. Both in males and females, patterns of CBT scores in non-right-handers with quadrant lesions are opposite to those found in right-handers. This suggests the existence of two functionally and neurally distinct cognitive selection mechanisms. Both mechanisms involve the frontal lobes, but their exact neuroanatomy depends on sex and handedness.