This paper discusses the impartiality issues that could arise within the UPC framework. After recalling the fundamental principles derived from the jurisprudence of the Court of Justice and the European Court of Human Rights, the risk of bias is identified: the issue of technical and part-time judges (mainly private practitioners) seems particularly problematic. Procedural guarantees do exist within the UPC framework, but don't appear sufficient : the practice of the UPC shall improve transparency and limit the risk of partiality, fundamental for the social acceptance and the functioning of the new Court.