Gene-gene　interaction　is　an　important　factor　to　consider　in　selecting　genes　in　genotype　data　or　microarray　expression　data　for　association　with　diseases.　However　current　definitions　of　gene-gene　interaction　are　not　very　clear　and　accurate.　An　inequality　is　proved　in　this　paper　and　a　new　definition　of　gene-gene　interaction:　conditional　independence　and　redundancy　based　definition　of　gene-gene　interaction　(CIR),　together　with　a　definition　of　interaction　group　are　proposed　according　to　this　inequality.　A　new　algorithm　to　detect　gene-gene　interaction　with　order　greater　than　two　is　also　proposed　based　on　these　new　definitions　and　a　theorem.　Experimental　results　show　the　usefulness　of　these　new　definitions　and　the　effectiveness　and　efficiency　of　this　new　algorithm.　©　2015　IEEE.