A method for enhancing the cleavage activity of an I-CreI derived meganuclease, comprising the site-specific mutation of at least one amino acid residue which is selected in the group consisting of: the glycine at position 19, the phenylalanine at position 54, the phenylalanine at position 87, the serine at position 79, the valine at position 105 and the isoleucine at position 132 of I-CreI, and its application for the manufacturing of meganuclease cleaving a DNA target of interest, for use in genome therapy (treatment of genetic diseases) and genome engineering (making of transgenic animals, transgenic plants and recombinant cell lines).