  We use the idea of expressing a nonoriented link as a sum of all oriented
links corresponding to the link to present a short proof of the
Lickorish-Millett-Turaev formula for the Kauffman polynomial at $z= -a-
a^{-1}$. Our approach explains the observation made by Lickorish and Millett
that the formula is the generating function for the linking number of a sublink
of the given link with its complementary sublink.
