We have tried to understand if the GDP convergence across the European Union, reflect also a convergence in terms of human development, as pointed out by more than one author. We have built a composite index, the ISUr (Regional Human development index) to rank the single regions of Europe in terms of human development, then we have focused our attention on the existence of b convergence (rate at which ISUr converges) between 1991 and 1996, and on the possible increase of dispersion of ISUr across the European Union (s convergence).