I don't have a whole lot to offer in the way of advice, but probably the biggest step is trying to find things to do that don't involve him. It sounds like they're trying to stay friends, but it doesn't seem to be working. Perhaps call him every once in a while, but not hang out, and then after a few months of only calling, maybe go back to hanging out.
You didn't say why they get mad at each other, but my guess would be that one of them brings up the relationship and why it failed, and/or one of them is still too attached to the other. Whichever one is attached needs to realize that the relationship is over, let it go, even though it's painful.