  Let $H$ be a separable complex Hilbert space. Denote by ${\mathcal
G}_{\infty}(H)$ the Grassmannian consisting of closed linear subspaces with
infinite dimension and codimension. This Grassmannian is partially ordered by
the inclusion relation. We show that every continuous order preserving
bijective transformation of ${\mathcal G}_{\infty}(H)$ is induced by an
invertible bounded semi-linear operator.
