PROBLEM TO BE SOLVED: To improve segmentation and time synchronization in the transmission of a multimedia digital data stream. SOLUTION: A multimedia stream server includes a cell-segmenting mechanism 90 for receiving a time stream(TS) packed from a storage device 26 and supplying a stand-by ATM cell 58A, a schedular 92, a related time wheel 94, an optionally specified high priority time wheel 96, and a data-supplying processor 98. Data are waited in a larger block, the mechanism 90 extracts the block and converts the block into an AAL-5 cell. Processing is executed by two boundaries, i.e., the fixed number N of MPEG-2TS packets acting as the maximum size of an AAL-5 frame and the inspection of a TS packet which includes a time synchronizing time stamp. The server allows the transmission of a data block detected by the time stamp to coincide with a time value indicated by the time stamp.