Only few of the Hungarian high school students intend to attend undergraduate programmes abroad, although their numbers show a growing trend in recent years. This is what IEER research examining the intentions of continuing education reveals, in addition to the fact that the Hungarian school system is unable to overcome the disadvantages caused by family background, that is, promote social mobility. Based on the 2013 National Skills Assessment the best national high schools receive only a very small proportion of students whose father has a low level of education or low labour market status. Our results also suggest that at the post-secondary level the education system reinforces existing inequalities. This can be concluded from the fact that the ratio of students who apply to the prestigious universities in Budapest is significantly lower in the lagging northern and lowland regions (even in the best high schools of these areas) than in the region of Central Hungary. The study was based on 770 responses conducted among the graduate students of thirty Hungarian public high schools, which were the best within their region according to the 2013 National Skills Assessment.