The conventional RZ-SSB demodulator consists of a limiter, FM demodulator and a linearizer. Since the conventional linearizer which cancels the high-order distortions must include Hilbert transformer, the performance of the demodulator are determined by the Hilbert transformer which is very complicated to realize in aeronautical telecommunication. This paper describes a method of designing RZ-SSB demodulator without Hilbert transformer. Since avionics systems are able to eliminate the inherent disadvantages in RZ-SSB, the results of this paper suggest that the RZ-SSB demodulator without Hilbert transformer is suitable for aeronautical telecommunication transceiver systems used in HF band.