In this study, we have investigated how the asymmetry of beat-to-beat foetal heart rate variability (fHRV) changes during development after 35 weeks and before 32 weeks of gestation. Noninvasive foetal electrocardiogram (fECG) signals from 78 pregnant women at the gestational age from 16 to 41 weeks with normal single pregnancies were analysed. Heart rate asymmetry (HRA) index that measures time asymmetry of RR interval time-series signal was used to understand the dynamics of fHRV. Results indicate that foetal HRA measured by Guzik's Index (GI) and Porta's Index (PI) changes after 35 weeks gestation compared to foetus before 32 weeks of gestation. It might be due to significant amount of maturation of the autonomic nervous system done after 35 and could potentially help identify the pathological autonomic nervous system development.