The lasing of a He-Ne laser in a transverse HF discharge at the 0. 63 mu m and 1. 15 mu m transitions has been investigated. The unsaturated gain coefficients chi //0 have been obtained. The dependence of chi //0 on the voltage amplitude and frequency of the HF field and on the total and partial pressures of the He-Ne mixture has been found. The plasma properties of the transverse HF discharge and a DC discharge in a hollow cathode have been established to be identical with respect to the radiation amplification at the stated transitions.