Disclosed are rationally-designed, non-naturally-occurring meganucleases in which a pair of enzyme subunits having specificity for different recognition sequence half-sites are joined into a single polypeptide to form a functional heterodimer with a non-palindromic recognition sequence. The invention also relates to methods of producing such meganucleases, and methods of producing recombinant nucleic acids and organisms using such meganucleases.