'unsystematically' originates from Modern English, specifically formed from the adjective 'unsystematic' (the negative prefix 'un-' + 'systematic'), where 'un-' meant 'not' and 'systematic' ultimately derives from Greek 'systema' meaning 'an organized whole'.

'unsystematic' was created by adding the negative prefix 'un-' to 'systematic' (which came into English via Late Latin 'systematicus' from Greek 'systematikos' and Greek 'systema'), and the adverb 'unsystematically' was formed by adding the adverbial suffix '-ally' to the adjective.

Initially, 'systematic' meant 'relating to or constituting a system' (from Greek 'systema'); over time adding 'un-' and '-ally' produced 'unsystematically', meaning 'in a way that does not follow a system'.