'non-amide-linked' is a modern compound formed from the negative prefix 'non-' + 'amide' + the past-participial adjective 'linked'. 'non-' comes from Latin/Old French usage meaning 'not' or 'without'; 'amide' is a chemical term from 19th-century chemical nomenclature; 'link' (past participle 'linked') is from the verb meaning 'to join'.

'amide' entered scientific English in the 19th century (from French and German chemical usage, related to 'ammonia' and the -ide suffix), while 'link' as a verb has roots in Old/Middle English meaning 'to fasten or connect'; the compound 'non-amide-linked' arose in modern chemical and biochemical literature by productive combination of these elements to describe connectivity.

The individual parts retained their basic senses ('non-' = not; 'amide' = the chemical group; 'linked' = joined), and together the compound's meaning—'not joined by an amide bond'—is a straightforward, literal extension used in technical contexts.