  We prove a new characterization of uniform hyperbolicity for fiber-bunched
cocycles. Specifically, we show that the existence of a uniform gap between the
Lyapunov exponents of a fiber-bunched $SL(2,\mathbb{R})$-cocycle defined over a
subshift of finite type or an Anosov diffeomorphism implies uniform
hyperbolicity. In addition, we construct an $\alpha$-H\"{o}lder cocycle which
has uniform gap between the Lyapunov exponents, however it is not uniformly
hyperbolic.
