Due to the high availability of large-scale annotated image datasets, knowledge transfer from pre-trained models showed outstanding performance in medical image classification. However, building a robust image classification model for datasets with data irregularity or imbalanced classes can be a very challenging task, especially in the medical imaging domain. In this paper, we propose a novel deep convolutional neural network, we called Self Supervised Super Sample Decomposition for Transfer learning (4S-DT) model. 4S-DT encourages a coarse-to-fine transfer learning from large-scale image recognition tasks to a specific chest X-ray image classification task using a generic self-supervised sample decomposition approach. Our main contribution is a novel self-supervised learning mechanism guided by a super sample decomposition of unlabelled chest X-ray images. 4S-DT helps in improving the robustness of knowledge transformation via a downstream learning strategy with a class-decomposition layer to simplify the local structure of the data. 4S-DT can deal with any irregularities in the image dataset by investigating its class boundaries using a downstream class-decomposition mechanism. We used 50,000 unlabelled chest X-ray images to achieve our coarse-to-fine transfer learning with an application to COVID-19 detection, as an exemplar. 4S-DT has achieved a high accuracy of 99.8% (95% CI: 99.44%, 99.98%) in the detection of COVID-19 cases on a large dataset and an accuracy of 97.54% (95%$ CI: 96.22%, 98.91%) on an extended test set enriched by augmented images of a small dataset, out of which all real COVID-19 cases were detected, which was the highest accuracy obtained when compared to other methods.