We present a novel outlier rejection scheme for point cloud registration using SE(3) voting on local transformation estimates with a dual consensus constraint. Point cloud registration is commonly performed by matching key-points in both point clouds and estimating the transformation parameters from these matches. In the presented method, each putative matching pair of points is equipped with a local transformation estimate using the Rigid Transformation Universal Manifold Embedding. Putative matching pairs with similar local estimates are then clustered together and the global transformation between point clouds is estimated for each cluster. Finally, the cluster with the majority of the votes such that the average of local transformations agrees with its associated global transformation is selected for completing the registration. This approach successfully deals with up to 99.5% outliers where state of the art fails.