This paper employs the Green's function method to investigate the stability of high-Reynolds-number Couette flow in the whole space. The core of the analysis relies on obtaining sharp estimates for the linearized Green's function. Based on these estimates, the study establishes a quantitative relationship between the transition threshold and the decay behavior of perturbations. Specifically, it proves that for any $0<\theta\leq\frac{1}{2}$, if the initial vorticity perturbation satisfies $$\|\omega_{0}\|_{L^{2}\cap L^1}\leq c_0\nu^{\frac{1}{2}(1+\theta)}$$ for some sufficiently small constant $c_0$ independent of the viscosity $\nu$, then the vorticity perturbation exhibits an enhanced decay rate of $(1+t)^{-(\frac{1}{2}+\theta)}$. Furthermore, the perturbation remains bounded within $O\left( \nu ^{\frac{1}{2}(1+\theta)}\right) $ of the underlying Couette flow.