Deep metric learning aims to learn embeddings that contain semantic similarity information among data points. To learn better embeddings, methods to generate synthetic hard samples have been proposed. Existing methods of synthetic hard sample generation are adopting autoencoders or generative adversarial networks, but this leads to more hyper-parameters, harder optimization, and slower training speed. In this paper, we address these problems by proposing a novel method of synthetic hard sample generation called symmetrical synthesis. Given two original feature points from the same class, the proposed method firstly generates synthetic points with each other as an axis of symmetry. Secondly, it performs hard negative pair mining within the original and synthetic points to select a more informative negative pair for computing the metric learning loss. Our proposed method is hyper-parameter free and plug-and-play for existing metric learning losses without network modification. We demonstrate the superiority of our proposed method over existing methods for a variety of loss functions on clustering and image retrieval tasks. Our implementations is publicly available.