We present measurements of high statistical significance of the rate of the magnetic octupole (M3 ) decay in nickel-like ions of isotopically pure 129Xe and 132Xe. On 132Xe, an isotope with zero nuclear spin and therefore without hyperfine structure, the lifetime of the metastable level was established as (15.06+/-0.24) ms. On 129Xe, an additional fast (2.7+/-0.1 ms) decay component was established that represents hyperfine mixing with a level that decays by electric quadrupole (E2 ) radiation.