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Douglas Harper's Etymology Dictionary
undeviating

1732, from un- (1) "not" + present participle of deviate.

Wiktionary
undeviating

a. 1 that does not deviate, veer or turn aside; unswerving 2 that does not change; steady

WordNet
undeviating
  1. adj. 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" [syn: unswerving]

  2. used of values and principles; not subject to change; steady; "undeviating loyalty"

Usage examples of "undeviating".

Not even the conversation of Madame de Rubine, nor the undeviating gentleness of her manners, could for a moment withdraw his thoughts from the painful contemplation of his real and imaginary distresses.

It was this deficiency, I considered, while running over in thought the perfect keeping of the character of the premises with the accredited character of the people, and while speculating upon th possible influence which the one, in the long lapse of centuries might have exercised upon the other -- it was this deficiency, perhaps, of collateral issue, and the consequent undeviating transmission, from sire to son, of the patrimony with the name, which had, at length, so identified the two as to merge the original title of the estate in the quaint and equivocal appellation of the ’.

He'd spent so much effort concentrating on keeping the great vehicle moving on an undeviating course, he'd neglected to check the gauges.

This I can positively assert was not the case, for Henriette was warmly and truly attached to him, and conducted herself as a wife with the most undeviating propriety.

Nayla recognized Moneo marching in the van, his uniform brilliant white, the even, undeviating stride with his gaze straight ahead.