The decision phase may be the most important phase of a biometric system. The human can be accepted or rejected based on the decision taken, that is built on a predefined threshold in the open-set systems, whereas in closed-set systems, the decision is built on the minimum score. Both systems have many drawbacks if they are performed separately. This paper presents a new identification system that combines the two systems. This combination offers all the advantages of both systems and overcomes their disadvantages. Consequently, this combination results new identification evaluation criteria. These new criteria are also described in this paper.