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Learning-based point cloud registration has achieved great success in recent years but is still limited by its generalization. The performance of these methods declines when they are extended to unseen datasets that have inconsistent distributions with the training set. In this paper, we propose a novel random network-based method, which does not require training. Our approach utilizes multiple randomly initialized networks for feature extraction and correspondence building. Furthermore, we also introduce a co-ensemble strategy to prune the outliers in correspondences built upon random networks, which leverages spatial consistency. Through our co-ensemble pruning, a large proportion of outliers can be removed, thereby achieving robust registration in affordable RANSAC iterations. Extensive experiments on 3DMatch and KITTI demonstrate that our method outperforms not only the traditional methods but also …