A method and apparatus for recording digital data streams. When a digital broadcast data stream received by a set top box is transmitted through a communication interface such as an IEEE-1394 bus to a streamer, program clock references contained in the data stream become different from the actual arrival time of the digital data stream because of different clock frequencies of the digital data stream and communication interface. The difference is compensated before the digital data stream is recorded on the streamer. The method in accordance with the present invention comprises detecting program clock references contained in received digital transport stream packets, creating the transport time reference of each transport stream packet based upon the detected program clock references and arrival times of the transport stream packets, and creating transport stream units by adding each of the created transport time reference to the associated transport stream packet.