  Controversy regarding whether Narrow Line Seyfert 1 galaxies (NLS1s) follow
the same black hole --- galactic bulge relation as normal galaxies has been
raised by Mathur et al. (2001) and Ferrarese et al. (2001). In this paper, the
correlation between the black hole mass and the velocity dispersion of the
narrow line region, indicated by the [OIII] line width for a heterogeneous
sample of NLS1s, is examined. We show that the non-virial component subtracted
[OIII] width, which may well represent the stellar velocity dispersion
($\sigma$), correlates with the estimated black hole mass $M_bh$, made using
the empirical law for broad line region sizefrom the reverberation mapping
measurements. Considering measurement errors, we find that the relation between
$M_bh$ and the [OIII] width in active galactic nuclei (both NLS1s in this paper
and normal Seyferts in Nelson 2000) is consistent with that defined in nearby
hot galaxies (ellipticals and spiral bulge) but with more scatter. It seems
that there is no clear difference in the relation between $M_bh$ and $\sigma$
(represented by the [OIII] width for AGN) in both NLS1s and normal broad line
active galactic nuclei from the same relation defined by nearby hot galaxies.
