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Improving the truthfulness of LLMs to alleviate hallucinations has become critical for promoting the practical deployment of LLMs. Current fine-tuning-based methods ignore the intrinsic discrepancy in the truthfulness correlations across LLM internal modules, and instead treat them equally, which may potentially decrease the performance of truthfulness improvement. In this paper, we propose a truthfulness-driven rank-adaptive LoRA method to improve LLM truthfulness (RaLFiT), which adaptively allocates the ranks in LoRA training according to the truthfulness correlations of modules within LLM. Specifically, it first measures the truthfulness correlation of each LLM module by a probing process, and allocates higher ranks to strongly correlated modules, which means a larger update subspace during training. Experimental results on TruthfulQA show that RaLFiT consistently outperforms previous state-of-the-art methods across the Llama LLM family, verifying its effectiveness and superiority, and for the first time makes the performance of 7B Llama LLMs exceed GPT-4.