We have analyzed the unusual electronic structure of Sr2FeMoO6 combining ab initio and model Hamiltonian approaches. Our results indicate that there are strong enhancements of the intra-atomic exchange strength at the Mo site as well as the antiferromagnetic coupling strength between Fe and Mo sites. We discuss the possibility of a negative effective Coulomb correlation strength ( U(eff)) at the Mo site due to these renormalized interaction strengths.