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In this paper, we investigate the cause of the high false positive rate in Visual Relationship Detection (VRD). We observe that during training, the relationship proposal distribution is highly imbalanced: most of the negative relationship proposals are easy to identify, e.g., the inaccurate object detection, which leads to the under-fitting of low-frequency difficult proposals. This paper presents Spatially-Aware Balanced negative pRoposal sAmpling (SABRA), a robust VRD framework that alleviates the influence of false positives. To effectively optimize the model under imbalanced distribution, SABRA adopts Balanced Negative Proposal Sampling (BNPS) strategy for mini-batch sampling. BNPS divides proposals into 5 well defined sub-classes and generates a balanced training distribution according to the inverse frequency. BNPS gives an easier optimization landscape and significantly reduces the number of false positives. To further resolve the low-frequency challenging false positive proposals with high spatial ambiguity, we improve the spatial modeling ability of SABRA on two aspects: a simple and efficient multi-head heterogeneous graph attention network (MH-GAT) that models the global spatial interactions of objects, and a spatial mask decoder that learns the local spatial configuration. SABRA outperforms SOTA methods by a large margin on two human-object interaction (HOI) datasets and one general VRD dataset.