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Human-Object Interaction (HOI) detection plays a crucial role in activity understanding. Though significant progress has been made, interactiveness learning remains a challenging problem in HOI detection: existing methods usually generate redundant negative H-O pair proposals and fail to effectively extract interactive pairs. Though interactiveness has been studied in both whole body- and part- level and facilitates the H-O pairing, previous works only focus on the target person once (i.e., in a local perspective) and overlook the information of the other persons. In this paper, we argue that comparing body-parts of multi-person simultaneously can afford us more useful and supplementary interactiveness cues. That said, to learn body-part interactiveness from a global perspective: when classifying a target person's body-part interactiveness, visual cues are explored not only from herself/himself but also from other persons in the image. We construct body-part saliency maps based on self-attention to mine cross-person informative cues and learn the holistic relationships between all the body-parts. We evaluate the proposed method on widely-used benchmarks HICO-DET and V-COCO. With our new perspective, the holistic global-local body-part interactiveness learning achieves significant improvements over state-of-the-art. Our code is available at https://github.com/enlighten0707/Body-Part-Map-for-Interactiveness.