This paper analyzes the evolution of the banking system sensitivity to cross-border contagion in 2006-2011. The study is performed on the basis of the BIS data on cross-border exposures and the Bankscope data on Tier 1 capital of 20 banking systems (Australia, Austria, Belgium, Canada, Finland, France, Germany, Greece, India, Ireland, Italy, Japan, the Netherlands, Portugal, Spain, Sweden, Switzerland, Turkey, the UK and the US). Since the European sovereign debt crisis took a decisive turn at the end of 2009, markets started looking at its main protagonists - Greece, Ireland, Italy, Portugal and Spain (GIIPS) - with a lot of anxiety. However, unexpectedly, we find that a single failure among GIIPS could be absorbed by the network. Our results reveal that the US, the UK, France and Germany pose the highest threat to the systemic stability. Moreover, the resilience of the banking systems to contagion risks tends to improve over the years.