  Einstein's theory of General Relativity predicts that the light from stars
will be gravitationally shifted to longer wavelengths. We previously used this
effect to measure the mass of the white dwarf Sirius B from the wavelength
shift observed in its H-alpha line based on spectroscopic data from the Space
Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope (HST), but
found that the results did not agree with the dynamical mass determined from
the visual-binary orbit. We have devised a new observing strategy using STIS
where the shift is measured relative to the H-alpha line of Sirius A rather
than comparing it to a laboratory based rest wavelength. Sirius A was observed
during the same orbit with HST. This strategy circumvents the systematic
uncertainties which have affected previous attempts to measure Sirius B. We
measure a gravitational redshift of 80.65 +/- 0.77 km/s. From the measured
gravitational redshift and the known radius, we find a mass of 1.017 +/- 0.025
Msol which is in agreement with the dynamical mass and the predictions of a C/O
white dwarf mass-radius relation with a precision of 2.5 per cent.
