Self Harm when having arguments

My fiance and I have been together for nearly 8 years. The last few years he's developed a problem where he'll hit himself when we get into arguments. He acknowledges the problem, but we don't know how to fix it. He doesn't want to seek professional help yet. Last night he gave himself a black eye. We want to fix this and work on things together. Does anyone have experience with this or can offer some advice?