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Abstract: large language models (LLMs) exhibit remarkable capabilities in various natural language processing tasks, such as machine translation. However, the large number of LLM parameters incurs significant costs during inference. Previous studies have attempted to train translation-tailored LLMs with moderately sized models by fine-tuning them on translation data. Nevertheless, when applying zero-shot translation directions not included in the fine-tuning data, the issue of ignoring instructions and thus translating into the wrong language, i.e., the off-target translation issue, remains unsolved. In this work, we design a two-stage fine-tuning algorithm to improve the instruction-following ability of translation-tailored LLMs, particularly for maintaining accurate translation directions. We first fine-tune LLMs on the translation dataset to elicit basic translation capabilities. In the second stage, we construct instruction-conflicting samples by randomly replacing the instructions with incorrect ones. Then, we introduce an extra unlikelihood loss to reduce the probability assigned to those samples. Experiments on IWSLT and WMT benchmarks using the LLaMA2 and LLaMA3 models, spanning 16 zero-shot directions, demonstrate that, compared to the competitive baseline-translation-finetuned LLaMA, our method could effectively reduce the off-target translation ratio (up to ?62.4%), thus improving translation quality (up to +9.7 BLEU). Analysis shows that our method can preserve the model's performance on other tasks, such as supervised translation and general tasks. Code is released at: https://github.com/alphadl/LanguageAware_Tuning.