  In this article, we present the results of a series of twelve 3.6-cm radio
continuum observations of T Tau Sb, one of the companions of the famous young
stellar object T Tauri. The data were collected roughly every two months
between September 2003 and July 2005 with the Very Long Baseline Array (VLBA).
Thanks to the remarkably accurate astrometry delivered by the VLBA, the
absolute position of T Tau Sb could be measured with a precision typically
better than about 100 micro-arcseconds at each of the twelve observed epochs.
The trajectory of T Tau Sb on the plane of the sky could, therefore, be traced
very precisely, and modeled as the superposition of the trigonometric parallax
of the source and an accelerated proper motion. The best fit yields a distance
to T Tau Sb of 147.6 +/- 0.6 pc. The observed positions of T Tau Sb are in good
agreement with recent infrared measurements, but seem to favor a somewhat
longer orbital period than that recently reported by Duchene et al. (2006) for
the T Tau Sa/T Tau Sb system.
