Use of machine learning for automatic analysis of job interview videos has recently seen increased interest. Despite claims of fair output regarding sensitive information such as gender or ethnicity of the candidates, the current approaches rarely provide proof of unbiased decision-making, or that sensitive information is not used. Recently, adversarial methods have been proved to effectively remove sensitive information from the latent representation of neural networks. However, these methods rely on the use of explicitly labeled protected variables (e.g. gender), which cannot be collected in the context of recruiting in some countries (e.g. France). In this article, we propose a new adversarial approach to remove sensitive information from the latent representation of neural networks without the need to collect any sensitive variable. Using only a few frames of the interview, we train our model to not be able to find the face of the candidate related to the job interview in the inner layers of the model. This, in turn, allows us to remove relevant private information from these layers. Comparing our approach to a standard baseline on a public dataset with gender and ethnicity annotations, we show that it effectively removes sensitive information from the main network. Moreover, to the best of our knowledge, this is the first application of adversarial techniques for obtaining a multimodal fair representation in the context of video job interviews. In summary, our contributions aim at improving fairness of the upcoming automatic systems processing videos of job interviews for equality in job selection.