  In a recent paper C. Miguel proved that the diameter of the commuting graph
of the matrix ring $\mathrm{M}_n(\mathbb{R})$ is equal to $4$ either if $n=3$
or $n>4$. But the case $n=4$ remained open, since the diameter could be $4$ or
$5$. In this work we close the problem showing that also in this case the
diameter is equal to $4$.
