We have investigated the pulse shortening problem of relativistic klystron amplifier. It is shown that non-working mode self-excitation is an important cause of pulse shortening. Theoretical and numerical analyses show the mechanism of non-working mode self-excitation caused by the coupling between cavities. By the use of radio frequency absorbers, the problem of non-working mode self-excitation can be solved. In the experiment, the RF output power is 920 MW, the output power pulse width of the device can be increased from 77 ns to 137 ns.