  We present epoch 1996, high-quality radial velocity data for HDE 226868, the
optical counterpart of Cygnus X-1. Combining our results with all published
historical data, we have derived a new ephemeris for the system of
HJD2450235.29 + n x 5.5998, which allows accurate orbital phase calculations to
be made for any X-ray observations over the last 30 years. We find no evidence
for any period change as has been suggested by Ninkov, Walker & Yang (1987). We
discuss the shortcomings of previous work in establishing the period and
orbital elements.
