  We study fixed loci of antisymplectic involutions on projective hyperk\"ahler
manifolds of $\mathrm{K3}^{[n]}$-type. When the involution is induced by an
ample class of square 2 in the Beauville-Bogomolov-Fujiki lattice, we show that
the number of connected components of the fixed locus is equal to the
divisibility of the class, which is either 1 or 2.
