Recently, a scheme for null space based linear discriminant analysis using random matrix multiplication (NSLDA/RMM) is proposed. The computational complexity of NSLDA/RMM is still relatively high since it need compute the eigenvalue decomposition of an n×n matrix, where n is the number of the training samples. To improve the efficiency of null space based linear discriminant analysis further, we present a new and fast scheme for null space based linear discriminant analysis using random matrix multiplication (FNSLDA/RMM). FNSLDA/RMM need not compute the eigenvalue decomposition of an n×n matrix. Then the computational complexity of FNSLDA/RMM is much lower than those of the existing schemes for null space based linear discriminant analysis. Theoretical analysis of computational complexity and experiments on face database demonstrate that FNSLDA/RMM is much more efficient than the existing schemes for null space based linear discriminant analysis, but the recognition rates of FNSLDA/RMM and the existing schemes for null space based linear discriminant analysis are the same.