There is disclosed a composition and a method for the efficient delivery of a therapeutic RNAi-inducing nucleic acid to cells both in vitro and in vivo through specific formulations of a non viral delivery system using chitosans. Particularly, the composition contains a nucleic acid and a specific chitosan that has the following physico-chemical properties: a number-average molecular weight between 5 kDa and 200 kDa, a degree of deacetylation between 80% and 95% and a chitosan amine to nucleic acid phosphate ratio below 20.