Anti-isomorphism of partially ordered sets

A bijective antitone mapping of a partially ordered set $A$ into a partially ordered set $B$, for which the inverse mapping is also antitone, i.e. a one-to-one mapping $\phi : A \rightarrow B$ such that $a < b$ ($a,b \in A$) implies $a\phi > b\phi$ in $B$ (and similarly for the inverse).