  Let $H$ be an infinite-dimensional complex Hilbert space and let ${\mathcal
L}(H)$ be the logic formed by all closed subspaces of $H$. For every natural
$k$ we denote by ${\mathcal G}_{k}(H)$ the Grassmannian consisting of
$k$-dimensional subspaces. An orthogonal apartment of ${\mathcal G}_{k}(H)$ is
the set consisting of all $k$-dimensional subspaces spanned by subsets of a
certain orthogonal base of $H$. Orthogonal apartments can be characterized as
maximal sets of mutually compatible elements of ${\mathcal G}_{k}(H)$. We show
that every bijective transformation $f$ of ${\mathcal G}_{k}(H)$ such that $f$
and $f^{-1}$ send orthogonal apartments to orthogonal apartments (in other
words, $f$ preserves the compatibility relation in both directions) can be
uniquely extended to an automorphism of ${\mathcal L}(H)$.
