The field-tuned ac susceptibility of Mn12Ac single crystal has been measured as functions of temperature and frequency. Two relaxation processes appear in our measurement. One is related to the magnetic quantum tunnelling of a collective spin S = 12 by a 61 K magnetic barrier and it has been well studied, while the other is faster than the former and its mechanism is unclear. We find that the relaxation time for the faster process shows the minima at H = 0 and H = 3.4 kOe, indicating that the quantum tunnelling also takes place in this process while the resonant fields are different from what we have known before.