Unconstrained on-line handwriting recognition is typically approached within the framework of generative HMM-based classifiers. In this paper, we introduce a novel discriminative method that relies, in contrast, on explicit grapheme segmentation and SVM-based character recognition. In addition to single character recognition with rejection, bi-characters are recognized in order to refine the recognition hypotheses. In particular, bi-character recognition is able to cope with the problem of shared character parts. Whole word recognition is achieved with an efficient dynamic programming method similar to the Viterbi algorithm. In an experimental evaluation on the Unipen-ICROW-03 database, we demonstrate improvements in recognition accuracy of up to 8% for a lexicon of 20,000 words with the proposed method when compared with an HMM-based baseline system. The computational speed is on par with the baseline system.