The frequency characteristics of a CuBr laser have been experimentally studied both in the regime of regular pulses emitted at a repetition frequency from several kilohertz to hundreds kilohertz and in the model regime of paired pulses emitted at a repetition frequency up to 30 kHz with a regulated time lag between pulses. The data obtained showed that the pulse repetition frequency as high as 500 kHz and even more can be achieved in a CuBr laser.