For many statistical pattern recognition methods, distributions of sample vectors are assumed to be normal, and the quadratic discriminant function derived from the probability density function of multivariate normal distribution is used for classification. However, the computational cost is $O(n^2)$ for $n$-dimensional vectors. Moreover, if there are not enough training sample patterns, covariance matrix can not be estimated accurately. In the case that the dimensionality is large, these disadvantages markedly reduce classification performance. In order to avoid these problems, in this paper, a new approximation method of the quadratic discriminant function is proposed. This approximation is done by replacing the values of small eigenvalues by a constant which is estimated by the maximum likelihood estimation. This approximation not only reduces the computational cost but also improves the classification accuracy.