This paper introduces a new noise generation algorithm for vocoder-based speech waveform generation. White noise is generally used for generating an aperiodic component. Since short-term white noise includes a zero-frequency component (ZFC) and inaudible components below 20 Hz, they are reduced in advance when synthesizing. We propose a new noise generation algorithm based on that for velvet noise to overcome the problem. The objective evaluation demonstrated that the proposed algorithm can reduce the unwanted components.