In previous research work, it has been reported that to obtain a high recognition rate in a printed Thai character recognition system, the system should be separated into two stages, namely rough and fine classification stages. In the rough classification stage, eigenvectors of the Karhunen-Loéve (K-L) expansion having the maximum eigenvalue are used as the standard patterns of each category of single-fount printed Thai characters, but the remaining eigenvectors which have been derived simultaneously were not used in that system. The same rough classification stage has been used in the paper. But in the fine classification stage, an experimental approach to fine classification, using higher-order eigenvectors (the remaining eigenvectors which were not used in rough classification) of the K-L expansion is described. Linear decision functions in the higher eigenvector space of the K-L expansion are constructed to discriminate between the characters in a category. The experimental results of recognising character patterns using the K-L expansion are shown in this paper.