  In this note, we study Shimura varieties for the groups $\mathrm{GU}(V)$,
where $V$ is a Hermitian space relative to a CM extension $E/E^+$. We give a
description of the supersingular locus of the fiber at a prime $\nu$ over $p$
of such a Shimura variety, under the assumptions that $\mathrm{dim}_E(V) \leq
4$ and that the prime $p$ splits completely in $E^+$ and is unramified in $E$.
