  Let $\La$ be an elementary locally bounded linear category over a field with
radical squared zero. We shall show that the bounded derived category
$D^b(\ModbLa)$ of finitely supported left $\La$-modules admits a Galois
covering which is the bounded derived category of almost finitely co-presented
representations of a gradable quiver. Restricting to the bounded derived
category $D^b({\rm mod}^b\hspace{-2pt}\La)$ of finite dimensional left
$\La$-modules, we shall be able to describe its indecomposable objects, obtain
a complete description of the shapes of its Auslander-Reiten components, and
classify those $\La$ such that $D^b({\rm mod}^b\hspace{-2.3pt}\La)$ has only
finitely many Auslander-Reiten components.
