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My advice is to make sure that you aren't dumping your current girlfriend for a new girlfriend. Make sure you are ending things with her because they aren't working out, then give yourself time before you start actually seeing this other girl. Otherwise, it'll be REALLY messy. My advice is to just tell her that things aren't working out. If they really aren't working out then it will be pretty evident for both of you. Mention that you're fighting too much. Say that the relationship isn't making you happy anymore. Just give her the truth, but don't make it harsh.