This paper proposes a novel metric that integrates confidence scores of correspondences, obtained through a Triangle Voting (TV) method, with correspondence-based metrics. The proposed metric assumes that a good hypothesis aligns correspondences with high-confidence scores very closely, thereby yielding higher score contributions. We further introduce two enhancement to improve the effectiveness of inlier-based metrics with confidence scores: (1) ignoring the distance of inliers with minor transformation errors, and (2) suppressing the erroneous high-score contributions caused by numerous low-confidence correspondences. Comparative experiments conducted on three datasets demonstrate the superiority of the proposed metric over all previously known correspondence-based metrics. The proposed metric achieves registration performance enhancements ranging from 1% to 16.95% and time savings ranging from 1.67% to 10.79% under default parameter settings. Moreover, it strikes a better balance among time consumption, robustness, and registration performance. Specifically, the improved inlier count metric exhibits highly robust and accurate performance. In conclusion, the proposed metric can accurately identify the more correct hypothesis during the hypothesis evaluation stage of RANSAC, thereby enabling precise point cloud registration.