Extreme points of unit balls in Lipschitz function spaces

We give a new characterization of the set $\mathop {\rm ext}\left ( B_{X^{\#}}\right )$ of all extreme points of the unit ball $B_{X^{\#}}$ in the Banach space $X^{\#}$ of all Lipschitz functions on a metric space $X.$ This result is applied to get a total variation characterization of $\mathop {\rm ext}\left ( B_{X^{\#}}\right )$ in the particular case when $X$ is a convex subset of a Banach space.