Definitions for unvarying
Random House Webster's College Dictionary
changeless, constant, invariant, unvarying(adj)
unvarying in nature
"maintained a constant temperature"; "principles of unvarying validity"
always the same; showing a single form or character in all occurrences
"a street of uniform tall white buildings"
persistent, constant or changeless
You can be sure of our unvarying attention.
lacking variety; having a uniform character
The prizewinning carrots were of an unvarying size.