  Large Language Models (LLMs) have achieved impressive results in Machine
Translation (MT). However, careful evaluations by human reveal that the
translations produced by LLMs still contain multiple errors. Importantly,
feeding back such error information into the LLMs can lead to self-refinement
and result in improved translation performance. Motivated by these insights, we
introduce a systematic LLM-based self-refinement translation framework, named
\textbf{TEaR}, which stands for \textbf{T}ranslate, \textbf{E}stimate,
\textbf{a}nd \textbf{R}efine, marking a significant step forward in this
direction. Our findings demonstrate that 1) our self-refinement framework
successfully assists LLMs in improving their translation quality across a wide
range of languages, whether it's from high-resource languages to low-resource
ones or whether it's English-centric or centered around other languages; 2)
TEaR exhibits superior systematicity and interpretability; 3) different
estimation strategies yield varied impacts, directly affecting the
effectiveness of the final corrections. Additionally, traditional neural
translation models and evaluation models operate separately, often focusing on
singular tasks due to their limited capabilities, while general-purpose LLMs
possess the capability to undertake both tasks simultaneously. We further
conduct cross-model correction experiments to investigate the potential
relationship between the translation and evaluation capabilities of
general-purpose LLMs. Our code and data are available at
https://github.com/fzp0424/self_correct_mt
