We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to 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 after taking perfections. Moreover, we study the intersections of the irreducible components. Stratifications of Deligne–Lusztig varieties defined using powers of Frobenius action appear in the description of the intersections.