Transformer-based approaches have demonstrated remarkable success in various sequence-based tasks. However, traditional self-attention models may not sufficiently capture the intricate dependencies within items in sequential recommendation scenarios. This is due to the lack of explicit emphasis on attention weights, which play a critical role in allocating attention and understanding item-to-item correlations. To better exploit the potential of attention weights and improve the capability of sequential recommendation in learning high-order dependencies, we propose a novel sequential recommendation (SR) approach called attention weight refinement (AWRSR). AWRSR enhances the effectiveness of self-attention by additionally paying attention to attention weights, allowing for more refined attention distributions of correlations among items. We conduct comprehensive experiments on multiple real-world datasets, demonstrating that our approach consistently outperforms state-of-the-art SR models. Moreover, we provide a thorough analysis of AWRSR's effectiveness in capturing higher-level dependencies. These findings suggest that AWRSR offers a promising new direction for enhancing the performance of self-attention architecture in SR tasks, with potential applications in other sequence-based problems as well.