The Youden Index is a summary measurement of the receiver operating characteristic (ROC) curve for the accuracy of a diagnostic test with ordinal or continuous endpoints. The bootstrap confidence interval based on the adjusted proportion estimate was shown to have satisfactory performance among the existing confidence intervals, including the parametric interval via the delta method. In this article, we propose two confidence intervals using the square-and-add limits based on the Wilson score method. We compare the two proposed intervals with the existing interval with extensive simulation studies. The new interval based on the empirical proportion estimate generally has better performance than that based on the adjusted proportion estimate. A real example from a clinical trial of prostate cancer is illustrated for the application of the new intervals.