  In this manuscript, we carefully check the correlation between the line width
and the line flux of the double-peaked broad H$\alpha$ of the well-known mapped
AGN 3C390.3, in order to show some further distinctions between double-peaked
emitters and normal broad line AGN. Based on the Virialization assumption and
the empirical relation about $R_{BLR}$, one strong negative correlation of line
parameters of the double-peaked broad lines should be expected for 3C390.3,
such as the negative correlation confirmed for the mapped broad line object
NGC5548. But, based on the public spectra around 1995 from the AGNWATCH project
for 3C390.3, one reliable positive correlation is found. In the context of the
proposed theoretical accretion disk model for double-peaked emitters, the
unexpected positive correlation can be naturally explained, due to different
time delays for inner parts and outer parts of disk-like BLR of 3C390.3.
Moreover, the Virialization assumption is checked and found to be still
available for 3C390.3. However, time-varying size of the BLR of 3C390.3 can not
be expected by the empirical relation $R_{BLR}\propto L^{\sim0.5}$, the
continuum emission strengthening leads to the size of BLR decreasing (not
increasing) in different moments for 3C390.3. Then, we compared our results of
3C390.3 with the previous results reported in the literature for the other
double-peaked emitters, and found that before to clearly correct effects from
disk physical parameters varying for long-term observed line spectra and
effects from the probable 'external' ionizing source with so far unclear
structures, it is hard to give one conclusion that the positive correlation can
be found for all double-peaked emitters. However, once one positive correlation
of broad line parameters was found, the accretion disk origination of the broad
line should be firstly considered.
