We study an extension of the MSSM by an anomalous abelian vector multiplet and a Stückelberg multiplet. The anomalies are cancelled by the Green-Schwarz mechanism and the addition of Chern-Simons terms. The advantage of this choice over the standard one is that it allows for arbitrary values of the quantum numbers of the extra U (1). As a first step towards the study of hadron annihilations producing four leptons in the final state (a clean signal which might be studied at LHC) we then compute the decays Z ′ → Z 0 γ and Z ′ → Z 0 Z 0 . We find that the largest values of the decay rate is ∼ 10 −4 GeV, while the expected number of events per year at LHC is at most of the order of 10.