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Recently computer-aided diagnosis methods have been widely adopted to aid doctors in disease diagnosis making their decisions more reliable and error-free. Electrocardiogram (ECG) is the most commonly used, noninvasive diagnostic tool for investigating various cardiovascular diseases. In real life, patients suffer from more than one heart disease at a time. So any practical automated heart disease diagnosis system should identify multiple heart diseases present in a single ECG signal. In this article, we propose a novel deep learning-based method for the multilabel classification of ECG signals. The proposed method can accurately identify up to two labels of an ECG signal pertaining to eight rhythm or morphological abnormalities of the heart and also the normal heart condition. Also, the black-box nature of deep learning models prevents them from being applied to high-risk decisions like the automated heart disease diagnosis. So in this article, we also establish an explainable artificial intelligence (XAI) framework for ECG classification using class activation maps obtained from the Grad-CAM technique. In the proposed method, we train a convolutional neural network (CNN) with constructed ECG matrices. With the experiments conducted, we establish that training the CNN by taking only one label for each ECG signal data point is enough for the network to learn the features of an ECG point with multilabel information in it (multiple heart diseases at the same time). During classification, we apply thresholding on the output probabilities of the softmax layer of our CNN, to obtain the multilabel classification of ECG signals.We trained the model with 6311 ECG records and tested the model with 280 ECG records. During testing, the model achieved a subset accuracy of 96.2% and a hamming loss of 0.037 and a precision of 0.986 and a recall of 0.949 and an F1-score of 0.967. Considering the fact that the model has performed very well in all the metrics of multilabel classification, the model can be directly used as a practical tool for automated heart disease diagnosis.