Using the averaged equations supplemented with 3D particle-in-cells simulation methods, we have studied the frequency multiplication regime in a high-current relativistic gyrotron. The paper shows that the ratio between the output power of the higher (fifth or sixth) harmonics and that of the fundamental cyclotron resonance may be of about 0.1-0.3%. Accordingly, the nonlinear transformation coefficient is several orders of magnitude higher than the values achievable in gyrotrons with weakly-relativistic electron beams. Keywords: gyrotron, harmonic excitation, high-current relativistic electron beams.