We have measured the rate of inelastic collisions in a cloud of doubly polarized ground-state cesium atoms (F = m(F) = 4) confined in a magnetic trap for temperatures T between 8 and 70 mu K. We find a two-body rate coefficient varying as T-0.63. At 8 mu K it reaches 4 X 10(-12) cm(3) s(-1) which is 3 orders of magnitude larger than predicted, ruling out a Bose-Einstein condensation of Cs in this internal state.