Serious debates ensued after the 2004 Taiwan presidential election and as a result a formal recounting process was implemented. In this paper, we proposed a mathematical model for the recounting. Our model is an extension of the one proposed by Harris (1988). Our basic assumption is that errors in misclassifying votes are due to unthought negligence. Denote by d the difference of the votes received by the two candidates. The distribution of d will be investigated. It is shown that under the basic assumption the recounting will not change the result of the election.