  We study the decomposability of Specht modules labelled by bihooks,
bipartitions with a hook in each component, for the Iwahori--Hecke algebra of
type $B$. In all characteristics, we determine a large family of decomposable
Specht modules, and conjecture that these provide a complete list of
decomposable Specht modules indexed by bihooks. We prove the conjecture for
small $n$.
