  In Finsler geometry, there are infinitely many models of constant curvature.
The Funk metrics, the Hilbert-Klein metrics and the Bryant metrics are
projectively flat with non-zero constant curvature. A recent example
constructed by the author is projectively flat with zero curvature. In this
paper, we introduce a technique to construct non-projectively flat Finsler
metrics with zero curvature in each dimension. The technique can be used to
construct many non-projectively flat Finsler metrics of constant curvature.
