LetPbe the transition matrix of a recurrent irreducible Markov chain onZ. We define a new Markov chain, modified fromP, with transition matrix [Ptilde](x,y=(1-α(x))P(x,y)plus;α(x,ywhere α(x) belongs to [0,1] andQis a Markovian matrix. IfPis positive recurrent, [Ptilde] is still positive recurrent if:where d is a distance onZdefined frompandman invariant measure byP. IfPis only recurrent, [Ptilde] is still recurrent with the condition (ii) alone for chainsPbelonging to a special class. In this class we find positive recurrent chains, random walks, chains whose jumps are bounded above by an exponential law.