'nonpalindrome' originates in modern English by combining the negative prefix 'non-' (from Latin 'non', meaning 'not') with 'palindrome', which ultimately traces to Greek 'palindromos' where 'palin-' meant 'again' and 'dromos' meant 'running'.

'palindrome' entered English via Classical/Medieval use of Greek 'palindromos' (παλίνδρομος) and later Latin/modern usages, becoming the English word 'palindrome'; 'nonpalindrome' is a modern English formation attaching 'non-' to 'palindrome' to indicate the negation.

Originally the Greek root described 'running back again' (literal motion), but in English 'palindrome' came to mean a sequence that reads the same backward and forward; 'nonpalindrome' correspondingly denotes a sequence that does not have that property.