  Let k be a perfect field. Recently J.-L. Colliot-Th\'el\`ene showed that two
pointless quadric surfaces over k are birationally equivalent if and only if
they are isomorphic. We show that this result holds for arbitrary del Pezzo
surfaces of degree $8$ with the Picard number $1$, and describe minimal
surfaces birationally equivalent to a given pointless del Pezzo surface of
degree $8$.
