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Weakly supervised object detection (WSOD) is a challenging task, in which image-level labels (e.g., categories of the instances in the whole image) are used to train an object detector. Many existing methods follow the standard multiple instance learning (MIL) paradigm and have achieved promising performance. However, the lack of deterministic information leads to part domination and missing instances. To address these issues, this paper focuses on identifying and fully exploiting the deterministic information in WSOD. We discover that negative instances (i.e. absolutely wrong instances), ignored in most of the previous studies, normally contain valuable deterministic information. Based on this observation, we here propose a negative deterministic information (NDI) based method for improving WSOD, namely NDI-WSOD. Specifically, our method consists of two stages: NDI collecting and exploiting. In the collecting stage, we design several processes to identify and distill the NDI from negative instances online. In the exploiting stage, we utilize the extracted NDI to construct a novel negative contrastive learning mechanism and a negative guided instance selection strategy for dealing with the issues of part domination and missing instances, respectively. Experimental results on several public benchmarks including VOC 2007, VOC 2012 and MS COCO show that our method achieves satisfactory performance.