To improve the performance of local learned descriptors, many researchers pay primary attention to the triplet loss network. As expected, it is useful to achieve state-of-the-art performance on various datasets. However, these local learned descriptors suffer from the inconsistency problem without considering the relationship between two descriptors in a patch. Consequently, the problem causes the irregular spatial distribution of local learned descriptors. In this paper, we propose a neat method to overcome the above inconsistency problem. The core idea is to design a triplet loss function of vertex-edge constraint (VEC), which takes the correlation between two descriptors of a patch into account. Furthermore, to minimize the non-matching descriptors' influence, we propose an exponential algorithm to reduce the difference between the long and short sides. The competitive performance against state-of-the-art methods on various datasets demonstrates the effectiveness of the proposed method.