the galaxy’s total stellar mass $M_*$ except at low stellar mass (${\rm log}(M_*/M_\odot) < 9.5$) and high specific SFR, they found a scatter of about 0.08 dex for the O3N2 estimator. In this work, we establish a new relation (Equation \[eq:sigma-z-fit\]), which is a modification of the MZR in [@Moustakas2011], to reinvestigate the local $\Sigma_*$ – $Z$ relation. We further take into account the contribution from the global $M_*$, and extend the Equation \[eq:sigma-z-fit\] to Equation \[eq:fmr-fit\] to reproduce the observed metallicity. As expected, the scatter in the $M_*$ – $\Sigma_*$ – $Z$ relation for all spaxels is significantly reduced. However, if excluding the low-mass (${\rm log}(M_*/M_\odot) < 9.5$) galaxies in the previous analyses, we find the reductive scatter from $\Sigma_*$ – $Z$ to $M_*$ – $\Sigma_*$ – $Z$ relation is much smaller. In Figure \[fig:plot\_residual\_mass\] of Appendix, we also plot the residuals between observed metallicity and the best fitted $\Sigma_*$ – $Z$ relations as a function of stellar mass for each metallicity index. The median values of the residuals with O3N2 ($middel$ panel) are in very good agreement with the results shown in the Fig.8 of [@Barrera-Ballesteros2016a]. We also note that, at the low stellar mass end, the $\Sigma_*$ 