Definitions for unswerving
Random House Webster's College Dictionary
going directly ahead from one point to another without veering or turning aside
"some people see evolution as an undeviating upward march from simple organisms to the very complex"; "a straight and narrow tree-lined road unswerving across the lowlands"
steadfast, staunch, unswerving(adj)
firm and dependable especially in loyalty
"a steadfast ally"; "a staunch defender of free speech"; "unswerving devotion"; "unswerving allegiance"
Not deviating; not yielding or straying or varying.
Origin: From un- + swerve + -ing.