'non-palindromic' originates from the English prefix 'non-' (meaning 'not', ultimately from Latin 'non') added to 'palindromic', which derives from Greek 'palindromos', where 'palin-' meant 'again' and 'dromos' meant 'running'.

'palindromic' comes from Greek 'palindromos' -> borrowed into English as 'palindrome/palindromic' (modern sense established by usage), and the English prefix 'non-' was later attached to form 'non-palindromic' to indicate the negative.

Initially the Greek root 'palindromos' carried the literal sense 'running back again'; over time 'palindromic' came to mean 'reads the same forwards and backwards', and 'non-palindromic' developed as the straightforward negative 'does not read the same forwards and backwards'.