  We analyse a manuscript star catalogue by Wilhem IV, Landgraf von
Hessen-Kassel, from 1586. From measurements of altitudes and of angles between
stars, given in the catalogue, we find that the measurement accuracy averages
26 arcsec for eight fundamental stars, compared to 49 arcsec of the
measurements by Brahe. The computation in converting altitudes to declinations
and angles between stars to celestial position is very accurate, with errors
negligible with respect to the measurement errors. Due to an offset in the
position of the vernal equinox the positional error of the catalogue is
slightly worse than that of Brahe's catalogue, but when correction is made for
the offset -- which was known to 17th century astronomers -- the catalogue is
more accurate than that of Brahe by a factor two. We provide machine-readable
Tables of the catalogue.
