  We present progress towards a new measurement of the electron electric dipole
moment using a cold supersonic beam of YbF molecules. Data are currently being
taken with a sensitivity of $10^{-27}\textrm{e.cm}/\sqrt{\textrm{day}}$. We
therefore expect to make an improvement over the Tl experiment of Commins'
group, which currently gives the most precise result. We discuss the systematic
and statistical errors and comment on the future prospect of making a
measurement at the level of $10^{-29}\textrm{e.cm}/\sqrt{\textrm{day}}$.
