  Let F be a function field of one variable over an algebraically closed field
of characteristic zero, X a geometrically irreducible smooth projective variety
over F, and L a line bundle on X. In this note, we will prove that if the
contangent bundle of X is ample and X is non-isotrivial, then there are a
proper closed algebraic set Y of X and a constant A > 0 such that h_L(P) <= A
d(P) + O(1) for all P \in X(\bar{F}) \ Y(\bar{F}), where h_L(P) is a geometric
height of P with respect to L and d(P) is the geometric logarithmic
discriminant of P. As corollary of the above height inequality, we can recover
Noguchi's theorem, i.e. there is a non-empty Zariski open set U of X with U(F)
= \emptyset.
