Abstract: This paper proposes a noval pattern discriminant method named class null subspace analysis of a range space (CNSA). CNSA obtains the range space of all available data. In the range space, the class null subspace (CNS) and the corresponding orthogonal complement of CNS for each class are defined. Both CNS and its corresponding orthogonal complement contain valid discriminant information. Since the within-class distance is zero in CNS, the distance between a sample of class i and the ith center would be much smaller than the distance from other center. For each class a proper projection matrix is constructed in CNSA. Not only samples of know classes can be classified, but a new sample, which is not included in known classes, can also be found by computing the distance between the test sample and the class mean vectors of the class feature spaces. The experimental results on terahertz time-domain spectroscopy (THz-TDS) data and COIL100 database verify the superiority of CNSA.