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This paper proposes a new voice activity detection (VAD) algorithm based on statistical noise suppression and framewise speech/non-speech classification. Although many VAD algorithms have been developed that are robust in noisy environments, the most successful ones are related to statistical noise suppression in some way. Accordingly, we formulate our VAD algorithm as a combination of noise suppression and subsequent framewise classification. The noise suppression part is improved by introducing the idea that any unreliable frequency component should be removed, and the decision can be made by the remaining signal. This augmentation can be realized using a few additional parameters embedded in the gain-estimation process. The framewise classification part can be either model-less or model-based. A model-less classifier has the advantage that it can be applied to any situation, even if no training data are available. In contrast, a model-based classifier (e.g., neural network-based classifier) requires training data but tends to be more accurate. The accuracy of the proposed algorithm is evaluated using the CENSREC-1-C public framework and confirmed to be superior to many existing algorithms.