'non-random' is formed from the negative prefix 'non-' plus the adjective 'random'. 'non-' is a negative prefix used in English (from Latin 'non' via Old French/Middle English) meaning 'not'.

'random' comes from Middle English 'randon' (meaning 'impetuosity, speed, or recklessness'), from Old French 'randon' / verb 'randir' meaning 'to run or move quickly'. Over time in English 'random' shifted to mean 'without definite aim or pattern'. The compound 'non-random' arose by combining the negative prefix with this adjective to denote 'not random'.

Originally 'random' related to rapid or impetuous movement; it later evolved to mean 'without definite aim' or 'by chance'. 'Non-random' therefore initially meant simply 'not by chance' and has come to be used especially in statistics and science to indicate systematic patterns or selection (including potential bias).