  For a Calabi-Yau variety X, Oguiso gave a useful criterion for primitivity of
a self-map of X in terms of the associated linear map on the Neron--Severi
space of X. In this short note, we prove a variant of Oguiso's criterion and
use it to verify primitivity of a certain birational automorphism of a
Calabi--Yau threefold, to which Oguiso's original criterion does not apply.
