Large language models (LLMs) have the potential to generate texts that pose risks of misuse, such as plagiarism, planting fake reviews on e-commerce platforms, or creating inflammatory false tweets. Consequently, detecting whether a text is generated by LLMs has become increasingly important. Existing high-quality detection methods usually require access to the interior of the model to extract the intrinsic characteristics. However, since we do not have access to the interior of the black-box model, we must resort to surrogate models, which impacts detection quality. In order to achieve high-quality detection of black-box models, we would like to extract deep intrinsic characteristics of the black-box model generated texts. We view the generation process as a coupled process of prompt and intrinsic characteristics of the generative model. Based on this insight, we propose to decouple prompt and intrinsic characteristics (DPIC) for LLM-generated text detection method. Specifically, given a candidate text, DPIC employs an auxiliary LLM to reconstruct the prompt corresponding to the candidate text, then uses the prompt to regenerate text by the auxiliary LLM, which makes the candidate text and the regenerated text align with their prompts, respectively. Then, the similarity between the candidate text and the regenerated text is used as a detection feature, thus eliminating the prompt in the detection process, which allows the detector to focus on the intrinsic characteristics of the generative model. Compared to the baselines, DPIC has achieved an average improvement of 6.76\% and 2.91\% in detecting texts from different domains generated by GPT4 and Claude3, respectively.