Large Language Models (LLMs) have shown great potential in Natural Language Processing (NLP) tasks. However, recent literature reveals that LLMs generate nonfactual responses intermittently, which impedes the LLMs' reliability for further utilization. In this paper, we propose a novel self-detection method to detect which questions that a LLM does not know that are prone to generate nonfactual results. Specifically, we first diversify the textual expressions for a given question and collect the corresponding answers. Then we examine the divergencies between the generated answers to identify the questions that the model may generate falsehoods. All of the above steps can be accomplished by prompting the LLMs themselves without referring to any other external resources. We conduct comprehensive experiments and demonstrate the effectiveness of our method on recently released LLMs, e.g., Vicuna, ChatGPT, and GPT-4.