To improve the computational efficiency of the kernel minimum squared error(KMSE) algorithm,we propose a fast KMSE by using the uncorrelated sample vectors,known as basic samples,in the feature space.And we describe the theoretical relationship between the linear correlation of sample vectors in the feature space and the determinant of the kernel matrix.The kernel functions between a sample and the basic samples were used to extract the features from the sample.The whole basic samples is only a small portion of the training set.The experiments on the intrusion detection dataset KDDCUP1999 and other benchmark datasets show that the fast KMSE is computationally efficient and can achieve high classification accuracy.