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Objective: Global (inter-patient) ECG classification for arrhythmia detection over Electrocardiogram (ECG) signal is a challenging task for both humans and machines. The main reason is the significant variations of both normal and arrhythmic ECG patterns among patients. Automating this process with utmost accuracy is, therefore, highly desirable due to the advent of wearable ECG sensors. However, even with numerous deep learning approaches proposed recently, there is still a notable gap in the performance of global and patient-specific ECG classification performances. This study proposes a novel approach to narrow this gap and propose a real-time solution with shallow and compact 1D Self-Organized Operational Neural Networks (Self-ONNs). Methods: In this study, we propose a novel approach for inter-patient ECG classification using a compact 1D Self-ONN by exploiting morphological and timing information in heart cycles. We used 1D Self-ONN layers to automatically learn morphological representations from ECG data, enabling us to capture the shape of the ECG waveform around the R peaks. We further inject temporal features based on RR interval for timing characterization. The classification layers can thus benefit from both temporal and learned features for the final arrhythmia classification. Results: Using the MIT-BIH arrhythmia benchmark database, the proposed method achieves the highest classification performance ever achieved, i.e., 99.21% precision, 99.10% recall, and 99.15% F1-score for normal (N) segments; 82.19% precision, 82.50% recall, and 82.34% F1-score for the supra-ventricular ectopic beat (SVEBs); and finally, 94.41% precision, 96.10% recall, and 95.2% F1-score for the ventricular-ectopic beats (VEBs).