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Electrode reversal errors in standard 12-lead electrocardiograms (ECG) can produce significant ECG changes and, in turn, misleading diagnoses. Their detection is important but mostly limited to the design of criteria using ECG databases with simulated reversals, without Wilson’s central terminal (WCT) potential change. This is, to the best of our knowledge, the first study that presents an algebraic transformation for simulation of all possible ECG cable reversals, including those with displaced WCT, where most of the leads appear with distorted morphology. The simulation model of ECG electrode swaps and the resultant WCT potential change is derived in the standard 12-lead ECG setup. The transformation formulas are theoretically compared to known limb lead reversals and experimentally proven for unknown limb–chest electrode swaps using a 12-lead ECG database from 25 healthy volunteers (recordings without electrode swaps and with 5 unicolor pairs swaps, including red (right arm—C1), yellow (left arm—C2), green (left leg (LL) —C3), black (right leg (RL)—C5), all unicolor pairs). Two applications of the transformation are shown to be feasible: ‘Forward’ (simulation of reordered leads from correct leads) and ‘Inverse’ (reconstruction of correct leads from an ECG recorded with known electrode reversals). Deficiencies are found only when the ground RL electrode is swapped as this case requires guessing the unknown RL electrode potential. We suggest assuming that potential to be equal to that of the LL electrode. The ‘Forward’ transformation is important for comprehensive training platforms of humans and machines to reliably recognize simulated electrode swaps using the available resources of correctly recorded ECG databases. The ‘Inverse’ transformation can save time and costs for repeated ECG recordings by reconstructing the correct lead set if a lead swap is detected after the end of the recording. In cases when the electrode reversal is unknown but a prior correct ECG recording of the same patient is available, the ‘Inverse’ transformation is tested to detect the exact swapping of the electrodes with an accuracy of (96% to 100%). Full article