A method for communication between a first communication terminal and a second communication terminal through a data forwarding unit connected to the first communication terminal and a destination data forwarding unit connected to the second communication terminal in a communication system, each of the data forwarding unit and the destination data forwarding unit adapted to be included in a network, the method comprising: at the first communication terminal, attaching information to compressed data obtained through compressing a header of original data destined for the second communication terminal, the information including a first information piece that indicates whether or not header extension processing of the compressed data by the data forwarding unit is required and that indicates, if the header extension processing of the compressed data is not required, the destination data forwarding unit which is the destination to which the data forwarding unit forwards the compressed data without extending the header, and a second information piece that indicates a forwarding route to the second communication terminal, the header extension processing of the compressed data being performed by the data forwarding unit by extending the compressed header in the compressed data when the compressed data is received by the data forwarding unit from the first communication terminal; and sending the compressed data to the data forwarding unit; and at the data forwarding unit, upon receipt of the compressed data from the first communication terminal, recognizing, based on the first information piece included in the information, whether or not the header extension processing of the compressed data is required, and recognizing, if the header extension processing of the compressed data is not required, based on the first information piece, the destination data forwarding unit which is the destination to which the data forwarding unit forwards the compressed data without extending the header, reading the second information piece from the information, and attaching the second information piece which is read from the information and a header for tunneling including address information of the destination data forwarding unit recognized from the second information piece to the compressed data of which the header extension processing is not required without extending the header, and sending the compressed data to a tunnel route for the destination data forwarding unit. at the first communication terminal, attaching information to compressed data obtained through compressing a header of original data destined for the second communication terminal, the information including a first information piece that indicates whether or not header extension processing of the compressed data by the data forwarding unit is required and that indicates, if the header extension processing of the compressed data is not required, the destination data forwarding unit which is the destination to which the data forwarding unit forwards the compressed data without extending the header, and a second information piece that indicates a forwarding route to the second communication terminal, the header extension processing of the compressed data being performed by the data forwarding unit by extending the compressed header in the compressed data when the compressed data is received by the data forwarding unit from the first communication terminal; and sending the compressed data to the data forwarding unit; and at the data forwarding unit, upon receipt of the compressed data from the first communication terminal, recognizing, based on the first information piece included in the information, whether or not the header extension processing of the compressed data is required, and recognizing, if the header extension processing of the compressed data is not required, based on the first information piece, the destination data forwarding unit which is the destination to which the data forwarding unit forwards the compressed data without extending the header, reading the second information piece from the information, and attaching the second information piece which is read from the information and a header for tunneling including address information of the destination data forwarding unit recognized from the second information piece to the compressed data of which the header extension processing is not required without extending the header, and sending the compressed data to a tunnel route for the destination data forwarding unit.