A new algorithm based on singular value decomposition (SVD) to remove cardiac contamination from trunk electromyography (EMG) is proposed. Its performance is compared to currently available algorithms at different signal-to-noise ratios (SNRs). The algorithm is applied on individual channels. An experimental calibration curve to adjust the number of SVD components to the SNR (0–20 dB) is proposed. A synthetic dataset is generated by the combination of electrocardiography (ECG) and EMG to establish a ground truth reference for validation. The performance is compared with state-of-the-art algorithms: gating, high-pass filtering, template subtraction (TS), and independent component analysis (ICA). Its applicability on real data is investigated in an illustrative diaphragm EMG of a patient with sleep apnea. The SVD-based algorithm outperforms existing methods in reconstructing trunk EMG. It is superior to the others in the time (relative mean squared error < 15%) and frequency (shift in mean frequency < 1 Hz) domains. Its feasibility is proven on diaphragm EMG, which shows a better agreement with the respiratory cycle (correlation coefficient = 0.81, p-value < 0.01) compared with TS and ICA. Its application on real data is promising to non-obtrusively estimate respiratory effort for sleep-related breathing disorders. The algorithm is not limited to the need for additional reference ECG, increasing its applicability in clinical practice.