Recent high precision measurements on the lifetime of the metastable 6s[3/2](2) state of atomic xenon display a difference with previous predictions by a factor of 2-3. In the present work, a systematic relaxation and correlation approach, which has been developed on the basis of a widely used multi-configuration Dirac-Fock method, is applied to study the electric dipole allowed El and forbidden M1, E2 and M2 transitions between the 5p(5)6s and 5p(6) configurations. We systematically include the correlation effects which arise from all the single and double excitations from the occupied {5s, 5p} shells into the {ns, np, (n - 1)d} (n = 6-10) active sets and the relaxation effects caused by change of the electron density between the radiative initial- and final-states. This study not only reduces greatly the existing discrepancy in the lifetime of the 6s[3/2](2) state, but also presents rather consistent results for both the lifetime of the metastable 6s '[1/2](o) state and the oscillator strength of the 5p(5)6s - 5p(6) E1 resonant transitions.