A fetal electrocardiogram (ECG) provides clinically significant information concerning the electrophysiological states of a fetus. Since the first attempt by Cremer in 1906, for about 100 years nobody has been able to non-invasively extract the fetal ECG popularly used in clinical situations. The low amplitude of the fetal signals and the high background noise and the non-linearity of the ECG signals mainly have been interfering with the noninvasive extraction of the fetal ECG. The aim of this paper is to introduce a new nonlinear filtering method to extract the fetal electrocardiogram detected from the mother's abdominal wall. This method consists of two steps: The rough extraction step performed by blind source separation (BSS) with references and the precise extraction step with fast non-linear state space projection (FNSSP) based on a nonlinear state space projection (NSSP), which needs several complicated conditions or has limitations. So, it takes a lot of time to calculate. Our new method does not require such conditions, and it has about a thirty-fold speedup when compared with the previous method. Our new method has been successfully applied to on-line recordings with fetal components and will be useful for monitoring the fetal electrocardiogram in clinical applications.