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Recent works show that local descriptor learning benefits from the use of L2 normalisation, however, an in-depth analysis of this effect lacks in the literature. In this paper, we investigate how L2 normalisation affects the back-propagated descriptor gradients during training. Based on our observations, we propose HyNet, a new local descriptor that leads to state-of-the-art results in matching. HyNet introduces a hybrid similarity measure for triplet margin loss, a regularisation term constraining the descriptor norm, and a new network architecture that performs L2 normalisation of all intermediate feature maps and the output descriptors. HyNet surpasses previous methods by a significant margin on standard benchmarks that include patch matching, verification, and retrieval, as well as outperforming full end-to-end methods on 3D reconstruction tasks.