The cheirality constraint, which requires that reconstructed point correspondences lie in front of the cameras, has not typically been integrated into traditional RANSAC-based pose estimators. We have developed a new RANSAC-based relative pose estimator which incorporates the cheirality constraint not only to preempt invalid epipolar geometry hypotheses, but also as a criterion in identifying inliers for image feature correspondences. Because the application of the cheirality constraint is tightly related to the estimation of epipolar geometry, integrating them inside RANSAC can prevent inliers being falsely identified as cheirality outliers. The result is a more consistent and stable estimation which leaves denser feature correspondences for subsequent processing. Experimental comparison between the usual RANSAC-based approach and the proposed approach is performed.