  The Dark Energy Spectroscopic Instrument (DESI) survey will provide optical
spectra for $\sim 3$ million quasars. Accurate redshifts for these quasars will
facilitate a broad range of science applications. Here we provide improved
systemic redshift estimates for the $\sim 95$k quasars included in the DESI
Early Data Release (EDR), based on emission-line fits to the quasar spectra.
The majority of the DESI pipeline redshifts are reliable. However, $\sim 19\%$
of the EDR quasars have pipeline redshifts that deviate from our new redshifts
by $>500\,{\rm km\,s^{-1}}$. We use composite quasar spectra to demonstrate the
improvement of our redshift estimates, particularly at $z>1$. These new
redshifts are available at
\url{https://github.com/QiaoyaWu/DESI_EDR_qsofit/blob/main/DESI_EDR_Aug29_redshift_only.fits}.
