  We define a second Steenrod square for virtual links, which is stronger than
Khovanov homology for virtual links, toward constructing
Khovanov-Lipshitz-Sarkar stable homotopy type for virtual links. This induces
the first meaningful nontrivial example of the second Steenrod square operator
on the Khovanov homology for links in a 3-manifold other than the 3-sphere.
