Recursive convolution has been used in conjunction with rational function approximation to significantly improve the efficiency of the transient analysis of lossy coupled transmission lines. Recursive convolution was first introduced in 1975 [1]. Recently, the method has been employed by a number of workers [2]-[6]. However, the algorithm has been mainly limited to distinct real poles. This paper presents a general algorithm for recursive convolution that includes complex conjugate pole pairs and high order real poles. These cases arise in the computation of the rational function approximations for lossy coupled transmission lines.