Pursuing a more coherent scene understanding towards real-time vision applications, single-stage instance segmentation has recently gained popularity, achieving a simpler and more efficient design than its two-stage counterparts. Besides, its global mask representation often leads to superior accuracy to the two-stage Mask R-CNN which has been dominant thus far. Despite the promising advances in single-stage methods, finer delineation of instance boundaries still remains unexcavated. Indeed, boundary information provides a strong shape representation that can operate in synergy with the fully-convolutional mask features of the single-stage segmenter. In this work, we propose Boundary Basis based Instance Segmentation(B2Inst) to learn a global boundary representation that can complement existing global-mask-based methods that are often lacking high-frequency details. Besides, we devise a unified quality measure of both mask and boundary and introduce a network block that learns to score the per-instance predictions of itself. When applied to the strongest baselines in single-stage instance segmentation, our B2Inst leads to consistent improvements and accurately parse out the instance boundaries in a scene. Regardless of being single-stage or two-stage frameworks, we outperform the existing state-of-the-art methods on the COCO dataset with the same ResNet-50 and ResNet-101 backbones.