Automatic recommendation systems based on deep neural networks have become extremely popular during the last decade. Some of these systems can, however, be used in applications that are ranked as High Risk by the European Commission in the AI act-for instance, online job candidate recommendations. When used in the European Union, commercial AI systems in such applications will be required to have proper statistical properties with regard to the potential discrimination they could engender. This motivated our contribution. We present a novel optimal transport strategy to mitigate undesirable algorithmic biases in multi-class neural network classification. Our strategy is model agnostic and can be used on any multi-class classification neural network model. To anticipate the certification of recommendation systems using textual data, we used it on the Bios dataset, for which the learning task consists of predicting the occupation of female and male individuals, based on their LinkedIn biography. The results showed that our approach can reduce undesired algorithmic biases in this context to lower levels than a standard strategy.