  We have measured the three-body decay of a Bose-Einstein condensate of
rubidium ($^{87}$Rb) atoms prepared in the doubly polarized ground state
$F=m_F=2$. Our data are taken for a peak atomic density in the condensate
varying between $2\times 10^{14}$ cm$^{-3}$ at initial time and $7\times
10^{13}$ cm$^{-3}$, 16 seconds later. Taking into account the influence of the
uncondensed atoms onto the decay of the condensate, we deduce a rate constant
for condensed atoms $L=1.8 (\pm 0.5) \times 10^{-29}$ cm$^{6} $s$^{-1}$. For
these densities we did not find a significant contribution of two-body
processes such as spin dipole relaxation.
