Let $K$ be a division ring with center $Z(K)$, and $n$ a positive integer. Let $\textrm{SL}(n,K)$ be the special linear group of degree $n$ over $K$ and $\textrm{SD}(n,K)$ its subgroup consisting of all diagonal matrices whose Dieudonne’s determinant is $\overline{1}$. We prove that $\textrm{SD}(n,K)$ is weakly pronormal, but not pronormal in $\textrm{SL}(n,K)$ provided either $Z(K)$ is an infinite field in case $n\ge 3$ or $Z(K)$ is a finite field containing at least seven elements in case $n\ge 5$.