  A Lie group is called $p$-regular if it has the $p$-local homotopy type of a
product of spheres. (Non)triviality of the Samelson products of the inclusions
of the factor spheres into $p$-regular $\mathrm{SO}(2n)_{(p)}$ is determined,
which completes the list of (non)triviality of such Samelson products in
$p$-regular simple Lie groups. As an application, we determine the homotopy
normality of the inclusion $\mathrm{SO}(2n-1)\to\mathrm{SO}(2n)$ in the sense
of James at any prime $p$.
