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1. An acronym for "High-Maintenance Non-Relationship". It refers to a relationship between two people of the opposite sex where one is dependent upon the other but there is no intimate or familial basis for the relationship between them.
Some also call it a "friendship".

2. A relationship a man has with a woman he isn't dating.
Julie called me five times last night cause her cat died. She's a great girl and all, but I totally have a HMNR with her.
by aegiswings August 04, 2005