  Recent studies on the environmental dependence of Type Ia supernova (SN Ia)
luminosity focus on the local environment where the SN exploded, considering
that this is more directly linked to the SN progenitors. However, there is a
debate about the local environmental, specifically local star formation rate
(SFR), dependence of the SN Ia luminosity. A recent study claims that the
dependence is insignificant ($0.051 \pm 0.020$ mag; $2.6\sigma$), based on the
local SFR measurement by fitting local $ugrizy$ photometry data. However, we
find that this photometric local SFR measurement is inaccurate. We argue this
based on the theoretical background of SFR measurement and the methodology used
to make that claim with their local $ugrizy$ photometry data, especially due to
a limited range of extinction parameters used when fitting the data. Therefore,
we re-analyse the same host galaxies with the same fitting code, but with more
physically motivated extinction treatments and global $ugriz$ photometry of
host galaxies. We estimate global stellar mass and SFR. Then, local star
formation environments are inferred by using the method which showed that SNe
Ia in globally passive galaxies have locally passive environments, while those
in globally star-forming low-mass galaxies have locally star-forming
environments. We find that there is significant local environmental dependence
of SN Ia luminosities: SNe Ia in locally star-forming environments are
$0.072\pm0.021$ mag ($3.4\sigma$) fainter than those in locally passive
environments, even though SN Ia luminosities have been further corrected by the
BBC method that reduces the size of the dependence.
