We report the measurement of the rate constant for dipolar relaxation from the (F=2, mF=2) hyperfine state of 7Li. The atoms are confined in a permanent magnet trap at a field of 103 G. The measured value of (1.05±0.10)×10−14 cm3/s agrees well with theory. Additionally, we determine an upper bound for the three-body molecular recombination rate constant of 10−27 cm6/s, which is also consistent with predictions.