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This paper describes a method of generating a stable walking trajectory for a biped humanoid robot. We design a desired ZMP trajectory by using a Fourier series, which has finite or infinite summation of sine and cosine functions, and calculating the coefficients of the Fourier series. And then, an analytic center of gravity (CoG) trajectory solution to the desired zero moment point (ZMP) trajectory is obtained by using the simple inverted pendulum model. A time segmentation-based approach is used to generate the desired ZMP trajectories. The coefficients of the sine and cosine functions are then calculated by using several conditions so that the desired ZMP trajectories are continuous between the segments. The paper also gives a proof of solution existence. To verify the effectiveness of the proposed method, we performed full-body dynamic simulation of a biped humanoid robot. The result confirmed the excellent performance of the proposed walking pattern generation method.