Abstract: For high-dimensional data, extraction of effective features is important for pattern recognition. Null-space linear discriminant analysis (NLDA) shows desirable performance, but it is still a linear technique in nature. In order to effectively extract nonlinear features of data set, a novel null-space kernel discriminant analysis (NKDA) is proposed for face recognition. Firstly, the kernel function is used to project the original samples into an implicit space called feature space by nonlinear kernel mapping. Then, the discriminant vectors in the null space of the kernel within-scatter matrix are extracted by only one step of economic QR decomposition. Finally, one step of Cholesky decomposition is used to obtain the orthogonal discriminant vectors in the kernel space. Compared with NLDA, not only does NKDA achieve better performance, but it is applicable to the large sample size problem. Besides, based on NKDA, the incremental NKDA method is developed, which can accurately update the discriminant vectors of NKDA when new samples are inserted into the training set. Experiments on ORL, Yale face database, and PIE subset demonstrate the effectiveness and efficiency of the algorithms, and show that the algorithm can reduce the dimensions of the data and improve the discriminant ability.