This paper describes a novel walking pattern generation method for a biped humanoid robot using convolution sum in discrete domain. For a biped walking model, single mass inverted pendulum model is generally used and the ZMP equation is described by decoupled linear differential equation. In the viewpoint of linear system response, walking pattern generation can be regarded as a convolution of an arbitrary reference ZMP and the walking pattern for an impulse ZMP. For the calculation of convolution, the walking pattern for an impulse ZMP is derived from the analytic walking pattern for a step ZMP. Then the convolution sum is derived in two recursive forms which can be applied in online and offline respectively. The proposed algorithm requires low computation power since the walking pattern equation is composed of a recursive form. Because the algorithm is expressed in analytic form, it is not required to solve optimization problem or calculate FFT as other researchers. Computer simulation of walking also shows excellent accuracy of the proposed algorithm compared to preview control method that have been regarded as an excellent one.