It is widely accepted that the Five Factor Model (FFM) is a satisfactory description of the pattern of covariations among personality traits, which supposedly fits, more or less adequately, every individual. As an amendment to the FFM, we propose that the customary five-factor structure is only a near-universal, because it does not fit all individuals but only a large majority of them. Evidences reveal a small minority of participants who have an unusual configuration of personality traits, which is clearly recognizable, both in self- and observer-ratings. We identified three types of atypical configurations of personality traits, characterized mainly by a scatter of subscale scores within each of the FFM factors. How different configurations of personality traits are formed, persist, and function needs further investigation.