Multi-view clustering (MVC) has garnered significant attention in recent studies. In this paper, we propose a novel MVC method, named CCL-MVC. The novel method constructs a cross-order neighbor tensor of multi-view data to recover a low-rank essential tensor, preserves noise-free, comprehensive, and complementary cross-order relationships among the samples. Furthermore, it constructs a consensus representation matrix by fusing the low-rank essential tensor with auto-adjusted cross-view diversity embedding, fully exploiting both consensus and discriminative information of the data. An effective optimization algorithm is developed, which is theoretically guaranteed to converge. Extensive experimental results confirm the effectiveness of the proposed method.