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Among many video tracking algorithms, Mean-shift has become the one that is drawing research attention worldwide. The author of this paper specifically deals with the incapability identified with Mean-shift to effectively track the fast state-varying object. Based on a given video sequence, in which the fast state-varying occurrences are observed and examined, a self-adaptive search window is accordingly engineered to eradicate the possible tracking failure due to non-overlap between the current search window and the previous one. The proposed search window can adapt its size in accordance with the instantaneous velocity of the target in motion, thus fix-sized bandwidth of the Mean-shift is modified in a self-adaptive manner. The test is presented showing that the proposed search window can function adequately well, resulting with satisfactory tracking quality.