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Deep metric learning (DML) aims to automatically construct task-specific distances or similarities of data, resulting in a low-dimensional representation. Several significant metric-learning methods have been proposed. Nonetheless, no approach guarantees the preservation of the ordinal nature of the original data in a low-dimensional space. Ordinal data are ubiquitous in real-world problems, such as the severity of symptoms in biomedical cases, production quality in manufacturing, rating level in businesses, and aging level in face recognition. This study proposes a novel angular triangle distance (ATD) and ordinal triplet network (OTD) to obtain an accurate and meaningful embedding space representation for ordinal data. The ATD projects the ordinal relation of data in the angular space, whereas the OTD learns its ordinal projection. We also demonstrated that our new distance measure satisfies the distance metric properties mathematically. The proposed method was assessed using real-world data with an ordinal nature, such as biomedical, facial, and hand-gestured images. Extensive experiments have been conducted, and the results show that our proposed method not only semantically preserves the ordinal nature but is also more accurate than existing DML models. Moreover, we also demonstrate that our proposed method outperforms the state-of-the-art ordinal metric learning method.