We present the results of echelle spectroscopy of the Lyalpha forest r
egion in the spectrum of the bright (m(R) = 18.5) optically selected z
= 4.5 QSO BR 1033 - 0327. These results, which extend Lyalpha forest
absorption line studies up to a redshift of z = 4.5 at a resolution of
12 km s-1, represent the first high-resolution study of Lyalpha fores
t systems at such high redshifts. We compare the properties of the Lya
lpha forest systems in the redshift range 3.7 < z < 4.3 with those inf
erred from similar observations at 1.86 < z < 3.27 and find some clear
indications of redshift dependence in these. First, the ionizing flux
from the quasar appears to affect the Lyalpha line density further fr
om the QSO than at lower redshifts, implying that the Lyman limit back
ground flux at redshift z approximately 4.2 is J(v) approximately 1-3
x 10(-22) ergs cm-2 s-1 Hz-1 sr-1. This is about a factor of 10 lower
than estimates at z approximately 2.5. Second, the Doppler parameter d
istribution for systems where the effect of the QSO ionizing flux is s
mall (3.7 < z < 4.3) has an excess at values approximately 20 km s-1,
compared with lower redshifts; we suggest this may be due to the lower
ionizing flux at z approximately 4.2 which would reduce the heating o
f the gas. Finally, while there is no evidence that the shape of the H
i column density distribution changes significantly, the redshift dep
endence of the total number of systems is stronger than that found at
lower redshifts, with the number of systems per unit redshift approxim
ately (1 + z)4.6. Also, over the entire redshift range there is no sig
nificant correlation between Doppler parameter and H I column density
and no signal in the two-point correlation function down to velocity s
eparations of DELTAv approximately 100 km s-1. There is no evidence fo
r continuously distributed H I absorption (the Gunn-Peterson effect) a
t these redshifts.