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We show that $t^{s/2} \Vert (\mbox{\boldmath $u$},\mbox{\boldmath$b$})(.,t)\Vert_{\dot{H}(\mathbb{R}^{n})} \rightarrow 0,$ as $t\rightarrow\infty$ for Leray solutions $(\mbox{\boldmath $u$}, \mbox{\boldmath $b$})(.,t)$of the incompressible MHD equations, where $2 \leq n \leq 4$ and $s \geq 0.$ Asa corollary of main result described previously we have also that$\lim_{t\rightarrow\infty} t^{\frac{n}{2} - \frac{n}{2q}} \Vert(\mbox{\boldmath$u$},\mbox{\boldmath $b$})(.,t)\Vert_{L^{q}(\mathbb{R}^{n})} = 0, 2\leq q\leq\infty.$

Decay Rates of global weak solutions for the MHD equations in $\dot{\mbox{\boldmath{$H$}}}^{s}(\mathbb{R}^n)$