Let $(ℝ,|\left|·\right|{\left|}_{\right)}$ be a Minkowski space with a unit ball and let ${\varrho }_H^{}$ be the Hausdorff metric induced by ${\left|\right|·\left|\right|}_{}$ in the hyperspace of convex bodies (nonempty, compact, convex subsets of ℝ). R. Schneider [RSP] characterized pairs of elements of which can be joined by unique metric segments with respect to ${\varrho }_H^{Bⁿ}$ for the Euclidean unit ball Bⁿ. We extend Schneider’s theorem to the hyperspace $(²,{\varrho }_H^{})$ over any two-dimensional Minkowski space.