  We have obtained optical intermediate resolution spectra (R = 3000) of the
narrow-line quasars DMS 0059-0055 and PG 1543+489. The [O III] emission line in
DMS 0059-0055 is blueshifted by 880 km/s relative to Hbeta. We also confirm
that the [O III] emission line in PG 1543+489 has a relative blueshift of 1150
km/s. These two narrow-line quasars show the largest [O III] blueshifts known
to date among type 1 active galactic nuclei (AGNs). The [O III] emission lines
in both objects are broad (1000 - 2000 km/s) and those in DMS 0059-0055 show
strong blue asymmetry. We interpret the large blueshift and the profile of the
[O III] lines as the result of an outflow interacting with circumnuclear gas.
Among type 1 AGNs with large blueshifted [O III], there is no correlation
between the Eddington ratios and the amount of [O III] blueshifts. Combining
our new data with published results, we confirm that the Eddington ratios of
the such AGNs are the highest among AGNs with the same black hole masses. These
facts suggest that the Eddington ratio is a necessary condition or the [O III]
blueshifts weakly depend on the Eddington ratio. Our new sample suggests that
there are possible necessary conditions to produce an outflow besides a high
Eddington ratio: large black hole mass (> 10^7 M_solar) or high mass accretion
rate (> 2 M_solar/yr) or large luminosity (lambda L_{lambda} (5100A) > 10^44.6
erg/s).
