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The accuracy of long-term position detection in dual-fiber optical trap is limited by low-frequency noise. We propose a technique that can reduce such noise. A position detection system for dual-fiber optical trap using a quadrant photodiode is built. The transmission light from the trapped particle is detected by two photodiodes. The normalized differential signal of transmission lights is demonstrated to carry the noise caused by asymmetric laser power fluctuation irradiating the microsphere, which is proved to dominate low-frequency noise. By subtracting this normalized difference from the position signal, the noise-reduction capability of this technique is remarkably 67% depending on detection bandwidth. It is expected to be applied to integrated and microfluidic fiber-optic trap system.