This paper describes an on-line Kanji character recognition method that solves the one-to-one stroke correspondence problem with both the stroke-number and stroke-order variations common in cursive Japanese handwriting. We propose two kinds of complementary algorithms: one dissolves excessive mapping and the other dissolves deficient mapping. Their joint use realizes stable optimal stroke correspondence without combinatorial explosion. Also, three kinds of inter-stroke distances are devised to deal with stroke concatenation or splitting and heavy shape distortion. These new ideas greatly improve the stroke matching ability of the selective stroke linkage method reported earlier by the authors. In experiments, only a single reference pattern for each of 2,980 Kanji character categories is generated by using training data composed of 120 patterns written carefully with the correct stroke-number and stroke-order. Recognition tests are made using the training data and two kinds of test data in the square style and in the cursive style written by 36 different people; recognition rates of 99.5%, 97.6%, and 94.1% are obtained, respectively. Moreover, comparative results obtained by the current OCR technique as applied to bitmap patterns of on-line character data are presented. Finally, future work for enhancing the stroke matching approach to cursive Kanji character recognition is discussed.