We study a dynamical system which describes the overlap of resonances in a global integrable context and we present a new topological scenario for the reconnection of three resonance island chains in the presence of two robust tori. These tori induce this new scenario and they play the role of transport barriers which are relevant for plasma confinement in Tokamaks.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)