Human embryonic stem cell research is a very promising area of human activity, which could lead to numerous breakthroughs in medicine. It also gives rise to many controversies mainly connected, but not limited to, the problem of exploitation and possible destruction of human embryos in the process of obtaining stem cells. The stance of European Union member states on the permissibility of such research is not uniform, it can however be financed (under some restrictions) from EU funds. By financing an area of activity the EU (or in fact any other institution) endorses such activity. However, in its judgement in case C-34/10 the Court of Justice of the European Union stated essentially that the exploitation of inventions based on human embryonic stem cells would be contrary to morality and ordre public, because the development of such inventions requires prior destruction or making use of an embryo. The described situation may be an example of an axiological inconsistency within the legal system of the EU, as its institutions clearly support an activity, not merely by tolerating it, but also by assigning funds to finance it, while at this same time, this activity is being regarded as immoral or threatening to ordre public, when it comes to granting patents. This article analyses current legal situation in regard to permissibility of human embryonic stem cell research within the EU and to the patentability of human embryonic stem cells and processes of obtaining them, in order to determine whether such inconsistency actually exists and what could be the possible consequences if it does exist.