This paper proposes a quadruplet loss and a corresponding deep network for person re-identification (ReID), aiming to improve the generalization ability of models. The triplet loss, commonly used in ReID, focuses on ordering images but struggles with generalization from training to testing data. The proposed quadruplet loss enhances inter-class variation and reduces intra-class variation, leading to better performance on testing sets. The quadruplet loss considers both correct ordering of pairs and pushing negative pairs away from positive pairs, with two margins controlling the balance between these aspects. A margin-based online hard negative mining strategy is introduced to select hard samples for training, improving model performance. The quadruplet network is evaluated on three datasets: CUHK03, CUHK01, and VIPeR. It outperforms most state-of-the-art methods, particularly in terms of rank-n accuracy. The method also shows better performance in reducing intra-class distances and increasing inter-class distances compared to the triplet loss. Theoretical analysis reveals that the quadruplet loss combines the strengths of both triplet and binary classification losses, leading to improved performance. The proposed method is effective in handling the challenges of person ReID, including large appearance variations and the need for generalization across different cameras. The results demonstrate that the quadruplet loss and network significantly enhance the performance of person ReID tasks.This paper proposes a quadruplet loss and a corresponding deep network for person re-identification (ReID), aiming to improve the generalization ability of models. The triplet loss, commonly used in ReID, focuses on ordering images but struggles with generalization from training to testing data. The proposed quadruplet loss enhances inter-class variation and reduces intra-class variation, leading to better performance on testing sets. The quadruplet loss considers both correct ordering of pairs and pushing negative pairs away from positive pairs, with two margins controlling the balance between these aspects. A margin-based online hard negative mining strategy is introduced to select hard samples for training, improving model performance. The quadruplet network is evaluated on three datasets: CUHK03, CUHK01, and VIPeR. It outperforms most state-of-the-art methods, particularly in terms of rank-n accuracy. The method also shows better performance in reducing intra-class distances and increasing inter-class distances compared to the triplet loss. Theoretical analysis reveals that the quadruplet loss combines the strengths of both triplet and binary classification losses, leading to improved performance. The proposed method is effective in handling the challenges of person ReID, including large appearance variations and the need for generalization across different cameras. The results demonstrate that the quadruplet loss and network significantly enhance the performance of person ReID tasks.