  We study the supersingular locus of a reduction at an inert prime of the
Shimura variety attached to $\mathrm{GU}(2,n-2)$. More concretely, we realize
irreducible components of the supersingular locus as closed subschemes of flag
schemes over Deligne--Lusztig varieties defined by explicit conditions.
Moreover we study the intersections of the irreducible components. A
stratification of Deligne--Lusztig varieties defined using a power of Frobenius
action appears in the description of the intersections.
