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Non-maximum suppression (NMS) is widely used in object detection pipelines for removing duplicated bounding boxes. The inconsistency between the confidence for NMS and the real localization confidence seriously affects detection performance. Prior works propose to predict Intersection-over-Union (IoU) between bounding boxes and corresponding ground-truths to improve NMS, while accurately predicting IoU is still a challenging problem. We argue that the complex definition of IoU and feature misalignment make it difficult to predict IoU accurately. In this paper, we propose a novel Decoupled IoU Regression (DIR) model to handle these problems. The proposed DIR decouples the traditional localization confidence metric IoU into two new metrics, Purity and Integrity. Purity reflects the proportion of the object area in the detected bounding box, and Integrity refers to the completeness of the detected object area. Separately predicting Purity and Integrity can divide the complex mapping between the bounding box and its IoU into two clearer mappings and model them independently. In addition, a simple but effective feature realignment approach is also introduced to make the IoU regressor work in a hindsight manner, which can make the target mapping more stable. The proposed DIR can be conveniently integrated with existing two-stage detectors and significantly improve their performance. Through a simple implementation of DIR with HTC, we obtain 51.3% AP on MS COCO benchmark, which outperforms previous methods and achieves state-of-the-art.