In recent years, electroencephalogram (EEG) signals have been used as a biometric modality, and EEG-based biometric systems have received increasing attention. However, due to the sensitive nature of EEG signals, the extraction of identity information through processing techniques may lead to some loss in the extracted identity information. This may impact the distinctiveness between subjects in the system. In this context, we propose a new self-relative evaluation framework for EEG-based biometric systems. The proposed framework aims at selecting a more accurate identity information when the biometric system is open to the enrollment of novel subjects. The experiments were conducted on publicly available EEG datasets collected from 108 subjects in a resting state with closed eyes. The results show that the openness condition is useful for selecting more accurate identity information.