  We describe a new method to calibrate the relative flux levels in spectra
from the HIRES echelle spectrograph on the Keck-I telescope. Standard data
reduction techniques that transfer the instrument response between HIRES
integrations leave errors in the flux of 5 - 10%, because the effective
response varies. The flux errors are most severe near the ends of each spectral
order, where there can be discontinuous jumps. The source of these errors is
uncertain, but may include changes in the vignetting connected to the optical
alignment. Our new flux calibration method uses a calibrated reference spectrum
of each target to calibrate individual HIRES integrations. We determine the
instrument response independently for each integration, and hence we avoid the
need to transfer the instrument response between HIRES integrations. The
procedure can be applied to any HIRES spectrum, or any other spectrum. While
the accuracy of the method depends upon many factors, we have been able to flux
calibrate a HIRES spectrum to 1% over scales of 200 A that include order joins.
We illustrate the method with spectra of Q1243+3047 towards which we have
measured the deuterium to hydrogen abundance ratio.
