  Let $\mathscr{L} \rightarrow X$ be an ample line bundle over a nonsingular
complex projective variety $X$. We construct an admissable flag $X_0 \subseteq
X_1 \subseteq...\subseteq X_n=X$ of subvarieties for which the associated
Okounkov body for $\mathscr{L}$ is a rational polytope.
