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Traditional MVS methods have good accuracy but struggle with completeness, while recently developed learning-based multi-view stereo (MVS) techniques have improved completeness except accuracy being compromised. We propose depth discontinuity learning for MVS methods, which further improves accuracy while retaining the completeness of the reconstruction. Our idea is to jointly estimate the depth and boundary maps where the boundary maps are explicitly used for further refinement of the depth maps. We validate our idea and demonstrate that our strategies can be easily integrated into the existing learning-based MVS pipeline where the reconstruction depends on high-quality depth map estimation. Extensive experiments on various datasets show that our method improves reconstruction quality compared to baseline. Experiments also demonstrate that the presented model and strategies have good generalization capabilities. The source code will be available soon.