Monitoring the fetal heart rate (fHR) and fetal electrocardiogram (fECG) during pregnancy is important to support medical decision making. Before labor, the fHR is usually monitored using Doppler ultrasound. This method is inaccurate and therefore of limited clinical value. During labor, the fHR can be monitored more accurately using an invasive electrode; this method also enables monitoring of the fECG. Antenatally, the fECG and fHR can also be monitored using electrodes on the maternal abdomen. The signal-to-noise ratio of these recordings is, however, low, the maternal electrocardiogram (mECG) being the main interference. Existing techniques to remove the mECG from these non-invasive recordings are insufficiently accurate or do not provide all spatial information of the fECG. In this paper a new technique for mECG removal in antenatal abdominal recordings is presented. This technique operates by the linear prediction of each separate wave in the mECG. Its performance in mECG removal and fHR detection is evaluated by comparison with spatial filtering, adaptive filtering, template subtraction and independent component analysis techniques. The new technique outperforms the other techniques in both mECG removal and fHR detection (by more than 3%).