Statistical characteristics of second order polarization mode dispersion (2 nd PMD) are investigated by Jones Transfer Matrix method. The model in which the value of PMD varies with step size in simulation is corrected. Using this corrected model, the frequency correlation function of PMD vector and the probability distribution of 2 nd PMD are obtained when the value of PMD is 25 ps; the results show good agreements with the theoretical prediction. It is necessary to higher order compensation in these conditions by analyzing the pulse broadening of an 8 ps width Gauss pulse briefly.