Knowledge Distillation (KD) has emerged as a pivotal technique for neural network compression and performance enhancement. Most KD methods aim to transfer dark knowledge from a cumbersome teacher model to a lightweight student model based on Kullback-Leibler (KL) divergence loss. However, the student performance improvements achieved through KD exhibit diminishing marginal returns, where a stronger teacher model does not necessarily lead to a proportionally stronger student model. To address this issue, we empirically find that the KL-based KD method may implicitly change the inter-class relationships learned by the student model, resulting in a more complex and ambiguous decision boundary, which in turn reduces the model's accuracy and generalization ability. Therefore, this study argues that the student model should learn not only the probability values from the teacher's output but also the relative ranking of classes, and proposes a novel Correlation Matching Knowledge Distillation (CMKD) method that combines the Pearson and Spearman correlation coefficients-based KD loss to achieve more efficient and robust distillation from a stronger teacher model. Moreover, considering that samples vary in difficulty, CMKD dynamically adjusts the weights of the Pearson-based loss and Spearman-based loss. CMKD is simple yet practical, and extensive experiments demonstrate that it can consistently achieve state-of-the-art performance on CIRAR-100 and ImageNet, and adapts well to various teacher architectures, sizes, and other KD methods.