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This paper presents a new method for noise-immune demodulation of BPSK signals. It is based on the use of an artificial neural network and signal randomization. Signal randomization increases self-synchronization properties and simplifies timing techniques. The demodulator model was designed and implemented in software. The demodulation bit error rate and standard deviation of normalized timing error were studied as a function of the signal-to-noise ratio. It was found out that the use of randomization reduces the normalized timing error by 7.5% at the normalized signal-to-noise ratio value of −15 dB. The method can be used to digital exchange data under strong interference conditions, in particular, in computer telecommunication systems, medical equipment, industrial networks, smart sensor networks and satellite communications.