Not of or pertaining to a relationship.(adjective)
Absence of relationship; unrelatedness.(noun)
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Use "nonrelationship" in a sentence
"For years after our pathetic nonrelationship, I had regretted my inexperience and lack of appeal, wondering if I could ever bridge the gap between insecure, unsure Andi and this confident Amanda person I should be in order to be truly dateable."
"No matter what kind of relationship or nonrelationship you had going, you were on the hook to somebody for something."
"Secondly, it denotes the actual nonrelationship “That was the worst hookup ever.”"