This study presents a novel approach to modeling the electrocardiogram (ECG): the Gaussian pulse decomposition. Constituent waves of the ECG are decomposed into and represented by Gaussian pulses using an iterative algorithm: the chip away decomposition (ChAD) algorithm. At each iteration, a nonlinear minimization method is used to fit a portion of the ECG waveform with a single Gaussian pulse, which is then subtracted from the ECG waveform. The process iterates on the resulting residual waveform until the normalized mean square error is below an acceptable level. Three different minimization methods were compared for their applicability to the ChAD algorithm; the Nelder-Mead simplex method was found to be more noise-tolerant than the Newton-Raphson method or the steepest descent method. Using morphologically different ECG waveforms from the MIT-BIH arrhythmia database, it was demonstrated that the ChAD algorithm is capable of modeling not only normal beats, but also abnormal beats, including those exhibiting a depressed ST segment, bundle branch block, and premature ventricular contraction. An analytical expression for the spectral contributions of the constituent waves was also derived to characterize the ECG waveform in the frequency domain. The Gaussian pulse model, providing an intuitive representation of the ECG constituent waves by use of a small set of meaningful parameters, should be useful for various purposes of ECG signal processing, including signal representation and pattern recognition.