Let $D$ be a division ring, and let $M $ be a free left $D$-module of finite rank. Assume that $x\mapsto x^*$ is an involution on the ring $\operatorname{End}_D(M)$ (which in this case means: ${}^*$ is a ring antiautomorphism [so $(xy)^* = y^* x^*$ for all $x,y$] whose square is the identity). Is ${}^*$ necessarily semilinear over $D$?
EDIT: If necessary, you may assume that $D$ is a division algebra over a field $K$, and that ${}^*$ is $K$-linear.