Person search is a composite task, aiming at locating and identifying a query person from uncropped images. It requires jointly solving Pedestrian Detection and Person Re-identification. One major challenge in person search is the contradictory goals of detection and re-identification. The model has to simultaneously model the universality and specificity of persons. In this paper, we propose a novel parameter-free approach called Feature Decomposition Person Search (FDPS) to separate various tasks. FDPS decomposes the ROI feature map to extract sub-features based on the marginal distribution for different tasks. Also, we find that the Online Instance Match loss pays imbalanced attention to positive and negative categories. We present a Balance Online Instance Match (BOIM) loss to enhance the contribution of negative categories during training. Our method achieves the state-of-the-art performance in one-step methods on two prevailing benchmarks, with high efficiency.