Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years, based on multivariate extreme-value theory. In this paper we present a tail dependence function and an extremal coefficient of dependence between two random vectors that extend existing ones. We shall see that in weakening the usual required dependence allows to assess the amount of dependence in d-variate random vectors based on bidimensional techniques. Simple estimators will be stated and can be applied to the well-known \emph{stable tail dependence function}. Asymptotic normality and strong consistency will be derived too. An application to financial markets will be presented at the end.