  We study two-dimensional Finsler metrics of constant flag curvature and show
that such Finsler metrics that admit a Killing field can be written in a normal
form that depends on two arbitrary functions of one variable. Furthermore, we
find an approach to calculate these functions for spherically symmetric Finsler
surfaces of constant flag curvature. In particular, we obtain the normal form
of the Funk metric on the unit disk D^2.
