Definition of non-unionize in US English:
non-unionize
(also non-unionise)
verb
rare
with object To make non-union in character; to withdraw recognition of a trade union from (a workforce or workplace).
Origin
Late 19th century; earliest use found in The New York Times. From non-union + -ize.
Pronunciation
non-unionize
/nɒnˈjuːnɪənʌɪz/