  We report upper limits on CO J=2--1 and CO J=5--4 emission from the quasar
SDSSp J104433.04-012502.2 at z=5.73 from observations made with the
Berkeley-Illinois-Maryland-Association Array. Previously reported limits on CO
J=6--5 emission (Iwata et al. 2001) were obtained at z=5.80, which is now
thought to be off by 1%, and the observations likely missed the relevant
redshifts for molecular gas. The new $3\sigma$ upper limits on the line
luminosities are $L^{'}_{CO}(2-1) < 5.1 \times 10^{10}$ K km s$^{-1}$ pc$^2$
and $L^{'}_{CO}(5-4) < 3.0 \times 10^{10}$ K km s$^{-1}$ pc$^2$, assuming 200
km s$^{-1}$ linewidth. The CO J=5--4 observations place an upper limit on warm,
dense molecular gas mass comparable to amounts derived for some other high
redshift quasar systems from detections of this line. The limit on CO J=2--1
emission suggests that excitation bias does not affect this conclusion. In
addition, no molecular gas rich companion galaxies are found in a $\sim1.4$ Mpc
field surrounding the quasar.
