Recent advancements in Large Language Models (LLMs) have showcased their remarkable capabilities in text understanding and generation. However, even stronger LLMs are susceptible to acquiring erroneous or obsolete information from the training corpus. Direct secondary fine-tuning with data containing new knowledge may be ineffective in updating knowledge due to the conflict between old and new knowledge. In this paper, we propose a new paradigm for fine-tuning called DFT (Delicate Fine-Tuning).This method utilizes parametric arithmetic to precisely pinpoint the location of knowledge and update only the minimal set of relevant parameters. Experimental results on two publicly available datasets demonstrate that our proposed DFT can obviously improve the knowledge updating performance of full fine-tuning , simultaneously outperforming the existing baselines in most cases.