We describe an approximate Green function decoupling theory for the dynamics of a dimerized Heisenberg chain. The theory retains the rotational invariance of the spin system in the approximations as Bulaevskii's approximate theory does not. We find that, within the approximations used, the excitation spectrum of the chain can be described as consisting of two branches: A band with a gap of k = 0 and a second, acoustic, band with no gap. The acoustic band does not appear in the Bulaevskii theory. We discuss the possible relevance of this result to experiments.