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Existing instance segmentation methods have achieved impressive performance but still suffer from a common dilemma: redundant representations (e.g., multiple boxes, grids, and anchor points) are inferred for one instance, which leads to multiple duplicated predictions. Thus, mainstream methods usually rely on a hand-designed non-maximum suppression (NMS) postprocessing step to select the optimal prediction result, which hinders endto-end training. To address this issue, we propose a box-free and NMS-free end-to-end instance segmentation framework, termed UniInst, that yields only one unique representation for each instance. Specifically, we design an instance-aware one-to-one assignment scheme, namely Only Yield One Representation (OYOR), which dynamically assigns one unique representation to each instance according to the matching quality between predictions and ground truths. Then, a novel prediction re-ranking strategy is elegantly integrated into the framework to address the misalignment between the classification score and the mask quality, enabling the learned representation to be more discriminative. With these techniques, our UniInst, the first FCN-based end-to-end instance segmentation framework, achieves competitive performance, e.g., 39.0 mask AP using ResNet-50-FPN and 40.2 mask AP using ResNet-101-FPN, against mainstream methods on COCO test-dev. Moreover, the proposed instance-aware method is robust to occlusion scenes, outperforming common baselines by remarkable mask AP on the * Equal Contribution