  In this paper, we are concerned with the compressible viscous
magnetohydrodynamic (MHD) system and investigate the large time behavior of
strong solutions near constant equilibrium. In the eighties, Umeda, Kawashima
and Shizuta initiated the dissipative mechanism for a rather general class of
symmetric hyperbolic-parabolic systems. From the point of view of
dissipativity, Kawashima in his doctoral dissertation established the optimal
time-decay estimates of $L^{q}$-$L^{2}(q\in [1,2)$) type for solutions to the
MHD system. Here, we shall improve Kawashima's efforts and give more precise
description for the large time asymptotic behavior of solutions, not only in
extra Lebesgue spaces but also in a full family of Besov norms with the
negative regularity index. Precisely, we show that the $L^{p}$ norm (the
slightly stronger $\dot{B}^{0}_{p,1}$ one in fact) of global solutions with the
critical regularity, decays like $t^{-d(\frac{1}{p}-\frac{1}{4})}$ for
$t\rightarrow\infty$. In particular, taking $p=2$ and $d=3$ goes back to the
classical time decay $t^{-\frac{3}{4}}$. We derive new estimates which are used
to deal with the strong coupling between the magnetic field and fluid dynamics.
