Uniqueness of geodesic imply no conjugate points?

Question

Let $M^n$ be a manifold diffeomorphic to $\mathbb R^n$, equipped with a complete Riemannian metric $g$. Suppose for any two points $p, q \in M$, there exists one and only one geodesic connecting $p$ to $q$. Does this imply that $g$ has not conjugate points? ps. the reverse is true.