The continuous Class-F Power Amplifier(PA) can mitigate the requirement of fundamental and second harmonic impedances by introducing a modified factor, thus extending the bandwidth of class-F PAs. In this paper, a new modified continuous Class-F mode is proposed. The design space is extended by introducing the resistive second and third harmonic impedance, so that it can realize multi-octave bandwidth. Based on this theory, an ultra-broadband high-efficiency power amplifier is realized showing 59%-79% drain efficiency,39.8-41.4 dBm saturation output power and large signal gain above 10 dB in 0.4-2.2 GHz frequency range. The simulation and test results are good, which verifies the validity of the methodology.