High-throughput　techniques　bring　novel　tools　and　also　statistical　challenges　to　genomic　research.　Identification　of　which　type　of　diseases　a　new　patient　belongs　to　has　been　recognized　as　an　important　problem.　For　high-dimensional　small　sample　size　data,　the　classical　discriminant　methods　suffer　from　the　singularity　problem　and　are,　therefore,　no　longer　applicable　in　practice.　In　this　article,　we　propose　a　geometric　diagonalization　method　for　the　regularized　discriminant　analysis.　We　then　consider　a　bias　correction　to　further　improve　the　proposed　method.　Simulation　studies　show　that　the　proposed　method　performs　better　than,　or　at　least　as　well　as,　the　existing　methods　in　a　wide　range　of　settings.　A　microarray　dataset　and　an　RNA-seq　dataset　are　also　analyzed　and　they　demonstrate　the　superiority　of　the　proposed　method　over　the　existing　competitors,　especially　when　the　number　of　samples　is　small　or　the　number　of　genes　is　large.　Finally,　we　have　developed　an　R　package　called　GDRDA　which　is　available　upon　request.