  The well-known Funk metric F(x,y) is projectively flat with constant flag
curvature K=-1/4 and the Hilbert metric H(x,y):=(F(x,y)+F(x,-y))/2 is
projectively flat with constant curvature K=-1. These metrics are the special
solutions to Hilbert's Fourth Problem. In this paper, we construct a
non-trivial R-flat spray using the Funk metric. It is then an inverse problem
in the calculus of variation to find a Finsler metric that induces the R-flat
spray. We find an explicit solution to this inverse problem and obtain a
non-trivial projectively flat Finsler metric with K=0.
