'non-peripteral' is formed from the prefix 'non-' (a Modern English negation) plus 'peripteral'. 'Peripteral' ultimately derives from Greek 'peripteros', where 'peri-' meant 'around' and 'pteron' meant 'wing' (used in architecture to denote a surrounding colonnade).

'Peripteros' (Greek) passed into Late Latin and Medieval Latin forms (e.g. 'peripterus'/'peripteralis'), entered English as 'peripteral' to describe temples with a surrounding row of columns, and later the negative prefix 'non-' was attached in Modern English to produce 'non-peripteral'.

The root originally described being 'surrounded by a single row of columns'; with the prefix 'non-' the meaning changed to 'not surrounded by such a row' and is used to describe buildings that lack a peripteral colonnade.