Lifetime measurements of the (3 − ), (4 − ), and (6 − ) intraband states in the neutron-rich, odd-odd 96 Rb nucleus were performed at the LOHENGRIN spectrometer of Institut Laue-Langevin, using thermal-neutron-induced fission of 235 U and fast-timing techniques with LaBr 3 : Ce scintillator detectors. The nanosecond isomeric nature of the (3 − ) bandhead was established as well as the β 2 = 0.39(3) deformation parameter of the band, pointing to a robust deformation in 96 Rb. Moreover, a hindered B(E 2) value of 3.9 +19 −13 × 10 −2 W.u. was found for the γ decay of the deformed (4 − ) state to the spherical 2 − ground state. A retardation was also found for the (3 − ) → 2 − transition, possibly due to the shape change and giving strong support to a shape coexistence scenario in this nucleus, at the borders of the island of deformation at N = 60. Analogies with the structure of the 98 Y isotone are discussed.