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It's a challenging task to design a high performance modulation for satellite and space communications due to the limited power and bandwidth resource. Constant envelope modulation is an attractive scheme to be used in such cases for their needlessness of input power back-off about 2~3 dB for avoidance of nonlinear distortion induced by high power amplifier. The envelope of Feher quadrature phase shift keying (FQPSK) has a least fluctuation of 0.18 dB (quasi constant envelope) and can be further improved. This paper improves FQPSK by defining a set of new waveform functions, which changes FQPSK to be a strictly constant envelope modulation. The performance of the FQPSK adopting new wave- form is justified by analysis and simulation. The study results show that the novel FQPSK is immune to the impact of HPA and outperforms conventional FQPSK on bit error rate (BER) performance. The BER performance of this novel modulation is better than that of FQPSK by more than 0.5 dB at least and 2 dB at most.