Extraction of the foetal electrocardiogram from single-channel maternal abdominal signals without disturbing its morphology is difficult. We propose to solve the problem by application of projective filtering of time-aligned ECG beats. The method performs synchronization of the beats and then employs the rules of principal component analysis to the desired ECG reconstruction. In the first stage, the method is applied to the composite abdominal signals, containing maternal ECG, foetal ECG, and various types of noise. The operation leads to maternal ECG enhancement and to suppression of the other components. In the next stage, the enhanced maternal ECG is subtracted from the composite signal, and this way the foetal ECG is extracted. Finally, the extracted signal is also enhanced by application of projective filtering. The influence of the developed method parameters on its operation is presented.