Fetal electrocardiograms (FECG) contain important indications about the health and condition of the fetus. In this respect, it is crucial to apply a robust algorithm to ECG data for extraction of the FECG signal. Most of the independent component analysis (ICA) algorithms used for this purpose rely on simple statistical models. Such algorithms can fail to separate desired signals when the assumed statistical model is inaccurate. Statistical models can be estimated accurately using kernel density estimation methods. Therefore, the kernel density estimation method was used in this paper for building an ICA algorithm (nonparametric ICA: NpICA) and the algorithm was applied to abdominal recordings to separate the FECG signals, which had not been implemented before. Checking of the separation quality of the NpICA algorithm was applied to synthetic ECG signals and real multichannel ECG recordings obtained from a pregnant woman's skin. The test results showed that the NpICA algorithm outperformed other known ICA algorithms such as FastICA and JADE. The superior performance of the NpICA algorithm was especially evident in recordings with high signal length. This indicates that the NpICA method is more robust than other classical ICA algorithms for FECG extraction.