  In this note we study the supersingular locus of the GU(2,2) Shimura variety
modulo a prime which is unramified in the imaginary quadratic extension. The
supersingular locus of this Shimura variety can be related to the basic
Rapoport-Zink space whose special fibre is described by the Bruhat-Tits
stratification. The description for this supersingular locus in the case where
the prime is inert in imaginary quadratic field is already known to Howard and
Pappas by exploiting the exceptional isomorphism. Our method is more direct
without using the exceptional isomorphism.
