The Eysenck Personality Questionnaire was completed by 4874 female and 2746 male Australian adults from the Australian Twin Register. Tetrachoric correlations between item responses were computed by maximum likelihood, and factor analysed. Stable Extraversion, Neuroticism and Social desirability ('Lie') factors were identified. In the four-factor solution, the fourth factor was clearly a Psychoticism factor, which had loadings greater than 0.2 on all but two of the items of the P scale. When more than four factors were estimated, however, this factor progressively split into Unconventional/impulsive behavior, suspiciousness, cruelty and punctuality factors. These P factors were stable across sexes and, in an oblique rotation, only moderately correlated. The factorial heterogeneity of the P scale is overlooked because of under-extraction of factors in the conventional 4-factor solution.