This paper proposes a new database management system that is called CDBMS(Communication Database Management System) for a communication robot DBMS for a communication robot has to satisfy following three conditions. The first condition is to make the internal states of a robot depend on robot's action. The second condition is to give priority to the execution of a reflective action. The third condition is to deal with the influence of past robot's actions. CDBMS satisfies the three conditions with C-Index and EDF scheduler. C-Index represents internal states as a directed graph which reflects a robot's current action and the sequence of past actions. Also, EDF scheduler achieves the prior execution of a reflective action. This paper conducted experiments which confirmed that CDBMS satisfies the first condition and the second condition.