This paper examines financial contagion, that is, whether the cross-market linkages in financial markets increases after a shock to a country. We introduce the use of a new measure of local dependence (introduced by Hufthammer and Tjøstheim (2009)) to study the contagion effect. The central idea of the new approach is to approximate an arbitrary bivariate return distribution by a family of Gaussian bivariate distributions. At each point of the return distribution there is a Gaussian distribution that gives a good approximation at that point. The correlation of the approximating Gaussian distribution is taken as the local correlation in that neighbourhood. By examining the local Gaussian correlation before the shock (in a stable period) and after the shock (in the crisis period), we are able to test whether contagion has occurred by a proposed bootstrap testing procedure. Examining the Mexican crisis of 1994, the Asian crisis of 1997-1998 and the financial crisis of 2007-2009, we find some evidence of contagion based on our new procedure.