Aims: Non-invasive fetal ECG (fECG) is a promising technique that could allow low-cost and risk-free diagnosis, and long-term monitoring. However, the low quality of the fECG extracted from non-invasive record-ings hampers its adoption in clinical practice. In this work, a new algorithm for the recovery of clean and morphologically preserved fECG signals from multi-channel trans-abdominal recordings is presented. Methods: The maternal ECG (mECG) is estimated in each channel by exploiting the optimal shrinkage and the nonlocal median algorithm ap-proaches, on a band-pass version of the abdominal signals. After a rough multi-channel fECG estimate by mECG subtraction from the abdominal re-cordings, a channel selection method, based on the agreement of two QRS detectors, is implemented to identify those in which the fetal QRS detection allows achieving robust results. On the selected fECG channels, the fetal R peaks were accurately identified by exploiting a de-shape short-time Fourier transform (dsSTFT) detector along with singular value decomposition and a pseudo-periodicity signal quality index. The identified R peaks were used as reference points to run the final post-processing stage by nonlocal median. Results: Three real 20 min-long four-channel abdominal ECG recordings from a public dataset were used for a preliminary performance assessment in terms of fetal QRS detection accuracy (ACC), true positive rate, positive predictive value and F1-score. Performance indexes were computed by com-paring the dsSTFT-based annotations obtained on the post-processed fECG signals with the real annotations. In these tests, the proposed algorithm was able to recover high-quality fECG traces from a morphological perspective, with very high performance also in terms of fetal QRS detection (median ACC and F1-score are 95.8% and 97.9%, respectively). Conclusion: The results obtained by the proposed algorithm suggest the possibility of successfully applying this approach for an effective non-invasive fECG extraction, deserving further investigations on larger real and synthetic datasets.