If you describe someone's attitude, feeling, or way of behaving as unswerving, you mean that it is strong and firm and does not weaken or change. In his diary of 1944 he proclaims unswerving loyalty to the monarchy. = unwavering. an unswerving belief or attitude is one that is very strong and never changes unswerving loyalty/commitment/support etc
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"