When using a finite DTV stream, discontinuity phenomena, such as a black or paused screen in the case of video and irregular or popping sounds in the case of audio, are generally experienced at the loop-back point. As the transmission time of the transport stream (TS) is commonly longer than the presentation time of video sequences, this causes an element stream (ES) buffer underflow at the loopback point of the TS. Therefore, this paper proposes a timematching multiplexing method for endless loop-back playing to resolve the discontinuity problem. Equations are developed to match the play times of the source, TS, and ES in consideration of the special TS transmission rate. In addition, new multiplexing methods are used to generate a TS to match the minimum matching time (MMT). Experimental results show that the MMT stream effectively eliminates any discontinuities.