Recent traffic measurements in corporate LANs, Variable-Bit-Rate (VBR) video sources, ISDN control channels, and other communication systems, have indicated traffic behavior of self-similar nature, which has implications for design, control and analysis of high-speed networks. Merging and splitting are two basic networking operations. This paper gave the necessary and sufficient conditions for that merging of second-order self-similar traffic streams also results in a second-order self-similar stream. It shows that splitting traffic streams of the second-order self-similar stream are still self-similar streams by the independent splitting operation.