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abstract: 'In this manuscript, we carefully check the correlation between the line width (second moment) 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 $M_{BH}\propto R_{BLR}\times V^2(BLR)$ and the empirical relation $R_{BLR}\propto L^{\sim0.5}$, one strong negative correlation between the line width and the line flux 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, $R_{BLR}\times V^2(BLR)\propto L^{\sim0.5}\times \sigma^2 = constant$. But, based on the public spectra around 1995 from the AGNWATCH project for 3C390.3, one reliable positive correlation is found between the line width and the line flux of the double-peaked broad H$\alpha$. 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 