Chinese is a representative East Asian language. Chinese Named Entity Recognition (CNER) aims to recognize various entities. It is significant for other NLP tasks to utilize CNER. Recent research to develop CNER systems has been dedicated to either considering word enhancement or capturing global information to strengthen local composition and alleviate word ambiguity in the meanings of words. However, information on words acquired from external lexicons is often confused, and this has led to incorrect judgments regarding the boundaries of words. Moreover, relevant studies typically use excessively complex models to capture the global semantics of sentences. To solve these two problems, we incorporate a global representation into the procedure of local word enhancement. We propose an intuitive and effective dual-module interactive network that can enhance the boundaries of words and extract the global semantics by using a rethinking mechanism to refine the importance of local composition and global information. The results of experiments on four CNER datasets showed that the proposed model can outperform other baselines in terms of the F1 score.