When a call from a call terminal to a called terminal is received, a relay processing device transmits calling terminal specific information that specifies the calling terminal to the called terminal by using data communication. The calling terminal specific information, for example, is a phone number of the calling terminal, but may be a user's name of the calling terminal. The called terminal transmits to the relay processing device, connection information that indicates whether or not to respond to the call from the calling terminal. The transmission of the connection information may be performed by any one of voice communication and data communication. The relay processing device connects the phone call between the called terminal and the calling terminal or cuts off the connection between the calling terminal and the relay processing device according to the connection information.