Finger-oximeters are ubiquitously used for patient monitoring in hospitals worldwide. Recently, remote measurement of arterial blood oxygenation (SpO2) with a camera has been demonstrated. Both contact and remote measurements, however, require the subject to remain static for accurate SpO2 values. This is due to the use of the common ratio-of-ratios measurement principle that measures the relative pulsatility at different wavelengths. Since the amplitudes are small, they are easily corrupted by motion-induced variations. We introduce a new principle that allows accurate remote measurements even during significant subject motion. We demonstrate the main advantage of the principle, i.e. that the optimal signature remains the same even when the SNR of the PPG signal drops significantly due to motion or limited measurement area. The evaluation uses recordings with breath-holding events, which induce hypoxemia in healthy moving subjects. The events lead to clinically relevant SpO2 levels in the range 80-100%. The new principle is shown to greatly outperform current remote ratio-of-ratios based methods. The mean-absolute SpO2-error (MAE) is about 2 percentage-points during head movements, where the benchmark method shows a MAE of 24 percentage-points. Consequently, we claim ours to be the first method to reliably measure SpO2 remotely during significant subject motion.