  In this paper we prove, if $\theta\in C([0,\infty),H^{2-2\alpha}(\mathbb
R^2))$ is a global solution of supercritical surface Quasi-Geostrophic equation
with small initial data, then $\|\theta(t)\|_{H^{2-2\alpha}}$ decays to zero as
time goes to infinity. Fourier analysis and standard techniques are used.
