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Cine cardiac magnetic resonance (CMR) has become the gold standard for the non-invasive evaluation of cardiac function. In particular, it allows the accurate quantification of functional parameters including the chamber volumes and ejection fraction. Deep learning has shown the potential to automate the requisite cardiac structure segmentation. However, the lack of robustness of deep learning models has hindered their widespread clinical adoption. Due to differences in the data characteristics, neural networks trained on data from a specific scanner are not guaranteed to generalise well to data acquired at a different centre or with a different scanner. In this work, we propose a principled solution to the problem of this domain shift. Domain-adversarial learning is used to train a domain-invariant 2D U-Net using labelled and unlabelled data. This approach is evaluated on both seen and unseen domains from the M\&Ms challenge dataset and the domain-adversarial approach shows improved performance as compared to standard training. Additionally, we show that the domain information cannot be recovered from the learned features.