\sigma_{new}^2 - \sigma^2$. Based on the listed values in Table 1, we can find that the common broadening velocity is around 20Å ($\sim1000{\rm km/s}$). Figure \[res2\] shows one example about the being broadened line profile. In the figure, we can find that the being broadened line profile (the IDL function ’convol’ being applied) with $\sigma_{b}=1000{\rm km/s}$ has begun to lead to some bad fitted results for the spectrum around the blue peak ($\sim6500$Å) of the double-peaked broad H$\alpha$, which indicates larger broadening velocity should be unreasonable. In other words, the varying range of the second moment is larger enough to ignore the effects of the uncertainty of the second moment on the positive correlation shown in Figure \[fj\_3c390\], and the positive correlation is reliable.

Besides the unexpected positive correlation shown in Figure \[fj\_3c390\] for 3C390.3, we wish to check the correlation of line parameters of broad lines for the other well-known mapped normal broad line AGN, in order to frankly show that the positive correlation for the double-peaked emitter 3C390.3 is very interesting. There are more than 40 nearby mapped objects reported in the literature (Barth et al. 2011, Bentz et al. 2006, 2009, 2010, Denney et al. 2006, 2009, 