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Synonyms for Unswerving (same or very similar meaning)

WordNet sense 1 (going directly ahead from one point to another without veering or turning aside):
undeviating

WordNet sense 2 (direct in spatial dimensions; proceeding without deviation or interruption; straight and short):
direct

WordNet sense 3 (firm and dependable especially in loyalty):
staunch, steadfast

WordNet sense 4 (steadfast in purpose or devotion or affection):
constant


From the ODE community, based on WordNetadd/edit