Non-invasive fetal ECG (fECG) is a promising technique that could allow low-cost and risk-free diagnosis, and long-term monitoring of fetal cardiac wellbeing. However, the low quality of the fECG extracted from non-invasive abdominal recordings 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. The proposed method exploits optimal shrinkage and nonlocal median algorithms, along with a de-shape short-time Fourier transform-based detection, to recover high-quality fECG traces from a morphological perspective, while ensuring very high performance also in terms of fetal QRS detection. On a small dataset, composed of three real 20 min-long four-channel abdominal ECG recordings, a preliminary performance assessment of the proposed fECG extraction method in terms of fetal QRS detection capabilities revealed a median accuracy of 95.8% and F1 score of 97.9%. The obtained results suggest the possibility of successfully applying this approach for an effective non-invasive fECG extraction, deserving further investigations on larger real and synthetic datasets.