Based on uncorrelated discriminant analysis, kernel uncorrelated discriminant analysis is developed. However, computing kernel uncorrelated vectors is computationally expensive due to the utilization of kernel functions. In order to overcome this problem, an effective method for solving kernel uncorrelated discriminant analysis is proposed in this paper. Firstly, the proposed algorithm smartly uses the decomposition of matrices. Then the generalized singular value decomposition on the matrix pair is carried out. At the same time, several related theorems are proposed. Most importantly, the proposed method can overcome the singular problem of matrices in kernel uncorrelated discriminant analysis. In some sense, the proposed method extends existing methods, namely, from linear problems to non-linear problems. Finally, experimental results on handwritten numeral characters show that the proposed method is effective and feasible.