'non-annual' is formed from the negative prefix 'non-' (from Latin 'non', meaning 'not') combined with 'annual' (from Latin 'annalis', from 'annus' meaning 'year').

'annual' entered English via Old French/Middle English from Latin 'annalis' (related to 'annus'). The prefix 'non-' comes directly from Latin 'non' and later productive in English compounding, producing the modern compound 'non-annual'.

Initially, 'annual' referred directly to 'of a year' or 'yearly'; the compounded form 'non-annual' developed to mean 'not yearly' or 'not occurring every year' and retains that negative, descriptive sense.