The method of determining an existence region of the non-equilibrium plasma of the pulsating negative corona and breakdown is developed. The low-temperature non-equilibrium pulsing plasma of the point-to-plane negative corona and a transition form to the breakdown in nitrogen-oxygen mixture are numerically simulated. It is shown that plasma parameters are pulsing in time as well as in space. In the phase of corona pulse peak, its position adjoins the cathode surface, no further than 0.01 cm. In the initial phase of breakdown, it extends far beyond the surface, within the distance of 0.03 cm. At the same time, the electron temperature changes in almost full anti-phase to the current: from 9100 K to 19000 K during the corona pulse peak and from 6000 K to 20000 K in initial phases of the breakdown. The average plasma density changes in the range 7 × 10 11 − 8 × 10 12 cm −3 in the first case and 1 × 10 13 − 5 × 10 13 cm −3 in the case of breakdown.