For matched-pair binary data, a variety of approaches have been proposed for the construction of a confidence interval (CI) for the difference of marginal probabilities between two procedures. The score-based approximate CI has been shown to outperform other asymptotic CIs. Tango's method provides a score CI by inverting a score test statistic using an iterative procedure. In this paper, we propose an efficient non-iterative method with closed-form expression to calculate Tango's CIs. Examples illustrate the practical application of the new approach.