Density Peak Clustering (DPC) often suffers from inaccurate center identification and chain assignment errors. Considering the aforementioned challenges, a new approach termed Second-Order K-Nearest Neighbor-based Density Peak Clustering (SOKNN-DPC) is introduced. The algorithm first re-plans the distance matrix to enhance intra-cluster compactness and inter-cluster separability. Then, representative points and second-order K-nearest neighbor densities are introduced to improve the robustness of center detection. Furthermore, a similarity matrix is constructed using Shared Nearest Neighbors (SNN), and a diffusion-based assignment strategy is designed to suppress chain errors. Theoretical analysis shows that the method maintains an O(n2) complexity. A series of evaluations conducted on various synthetic and UCI benchmarks confirm that SOKNN-DPC consistently outperforms DPC, SNN-DPC, DBSCAN, and K-means. This study provides a new perspective for improving density-based clustering by jointly enhancing center identification and assignment stability.