Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
HALIBURTON
As described in historical dictionaries
Patronymica Britannica (1860)
HALIBURTON. "The )rincipal old family of this name was Halyburton, of that Ilk, in the shire of Berwick. The chappel of Halyburton was a pendicle of the church of Greenlaw." Nisbet. The family are mentioned so early us the reign of King Malcolm IV.