Complete independence of an axiom system for central translations

A recently proposed axiom system for Andr\'e's central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed independent. Second, whereas most of the original independence models were infinite, finite independence models are available. Moreover, the independence proof for one of the axioms employed proof-theoretic techniques rather than independence models; for this axiom, too, a finite independence model exists. For every axiom, then, there is a finite independence model. Finally, the axiom system (without its single dependent axiom) is not only independent, but completely independent.