  In this note, we provide a characterization for the set of extreme points of
the Lipschitz unit ball in a specific vectorial setting. While the analysis of
the case of real-valued functions is covered extensively in the literature, no
information about the vectorial case has been provided up to date. Here, we aim
at partially filling this gap by considering functions mapping from a finite
metric space to a strictly convex Banach space that satisfy the Lipschitz
condition. As a consequence, we present a representer theorem for such
functions. In this setting, the number of extreme points needed to express any
point inside the ball is independent of the dimension, improving the classical
result from Carath\'eodory.
