Abstract: The paper has discussed such problims as the properties of sub-eigenvalue and sub-eigenvector of real-anti-sub-symmetric matrix,and its diagonalization.Based on the above,the following result could be approached:If Ais a realanti-sub-symmetric matrix,then there exists a perpendicular matrix P.Multiplied with P and its reversal PSTfrom the right and the left respectively,the matrix will become a diagonalmatrix.