In this paper, we identify a new category of bias that induces input-conflicting hallucinations, where large language models (LLMs) generate responses inconsistent with the content of the input context. This issue we have termed the false negative problem refers to the phenomenon where LLMs are predisposed to return negative judgments when assessing the correctness of a statement given the context. In experiments involving pairs of statements that contain the same information but have contradictory factual directions, we observe that LLMs exhibit a bias toward false negatives. Specifically, the model presents greater overconfidence when responding with False. Furthermore, we analyze the relationship between the false negative problem and context and query rewriting and observe that both effectively tackle false negatives in LLMs.