The invention provides methods and means for specifically altering the DNA sequence in a genome, in particular for genome editing by deleting or replacing a sequence of interest. Advantageously, the invention uses two non-identical sequences naturally occurring in a genome as target sites two which DNA-recombining enzymes are generated. The invention is in particular useful for medicine, in particular to repair a mutation in a genome or to delete predefined genetic material from cells or tissue and to cure diseases. An advantage of the invention is that it allows precise site directed altering of DNA without engaging host DNA repair pathways and thereby works without inducing random insertions and deletions (indels).