The structure of the low-lying states with negative parity of3793Rb56 has been studied in the framework of the Interacting Boson-Fermion Model (IBFM) using the even-even neighbour3894Sr56 as a core. A good description of the properties of the levels has been obtained. A sensitive test of the quality of the theoretical studies is the decay pattern of the second excited state at 267 keV with a half-life of 2.0(2) ns. The calculations givet1/2=2.26 ns and they predict the existence of a 13 keV transition into the first excited state, the existence of which has been confirmed afterwards by experiments.