Late Roman Ordo or Maniple?

[Longovicium]

I have an old copy of Phil Barker's 'Armies and Enemies of Imperial Rome' on my shelf and have always used his illustration of the 'rough' structure of the late legio as a basis on which to hang my writing. However, lately I have begun to wonder about his use of the 'ordo' as unit descriptor of what used to be referred to as the maniple. I know Ammianus frequently uses the maniple as his preferred term and that has been seen as a classicising bent in his writings - therefore 'maniple' did not accurately reflect contemporary Roman usage. I wonder if anyone here can point out exactly where the 'ordo' or 'ordine' comes from or if Barker's use of the term has now been superseded?

I would be grateful if the 'ordo' term could be illustrated with references, if is is a viable late Roman military term, as I am begining to loose confidence in deploying it!