  Millions of quasar spectra will be collected by the Dark Energy Spectroscopic
Instrument (DESI), leading to a four-fold increase in the number of known
quasars. High accuracy quasar classification is essential to tighten
constraints on cosmological parameters measured at the highest redshifts DESI
observes ($z>2.0$). We present the spectral templates for identification and
redshift estimation of quasars in the DESI Year 1 data release. The quasar
templates are comprised of two quasar eigenspectra sets, trained on spectra
from the Sloan Digital Sky Survey. The sets are specialized to reconstruct
quasar spectral variation observed over separate yet overlapping redshift
ranges and, together, are capable of identifying DESI quasars from $0.05 < z
<7.0$. The new quasar templates show significant improvement over the previous
DESI quasar templates regarding catastrophic failure rates, redshift precision
and accuracy, quasar completeness, and the contamination fraction in the final
quasar sample.
