The french minimum income (RMI) remains stable in real terme since its creation in 1988, but was depreciated in relation to law wages and particularly to minimum wage (the Smic). This evolution seems to justify the revaluation according to relative poverty approach. But as Rmi is a differential allocation completed by a temporary incentive mechanism, a revaluation could lead to emphasize the poverty trap problem. We discuss the effectiveness of poverty trap in the french case in a context of massive unemployment and part time jobs increase.