A new analysis of the relation between the damping of the Collette torsion pendulum and the internal friction of the specimen is given. It is shown that the existing theories both of Collette et al. and of Iwasaki et al are insufficient and give incorrect results. A better and more general damping formula is derived and confirmed by experiment. Contrary to the work of Iwasaki et al, a broad range of applicability of the Collette pendulum within its possible frequency interval is found.