This paper describes a pipelining universal system of discrete time cellular neural networks (DTCNNs). The new relaxation-based algorithm which is called a Pipelining Gauss Seidel (PGS) method is used to solve the CNN state equations in pipelining. In the systolic system of N processor elements {PEi}, each PEi performs the convolusional computation (CC) of all cells and the preceding PEi-1 performs the CC of all cells taking precedence over it by the precedence interval number p. The expected maximum number of PE's for the speeding up is given by n/p where n means the number of cells. For its application, the encoding and decoding process of moving images is simulated.