Let $A$ be a hereditary algebra and let $\mathcal{D}$ be the derived category of bounded complex of finitely generated $A$-modules. Then, for any complex $C_{\bullet}$ in $\mathcal{D}$, we have $C_{\bullet} \cong H_{\bullet}(C_{\bullet})$, where the right hand side is the complex whose $i$-th term is $H_i(C_{\bullet})$ and all of whose maps are zero.