In this paper, we discuss the problem of two stationary solutions of the Liouville equation when an external field is present. We show that the key point for calculating the transport coefficient by the Kubo formula is: before completing the integral over time, the time behavior of the correlation function must be expressed in terms of the theory of approach to equilibrium. With this point, being considered, it is then possible to derive the correct expression for transport coefficient. Using this method, we calculate once again the conductivity under strong magnetic field that had been discussed in reference [1], and obtain a correct non-vanishing result.