Iterative closest point (ICP) is a popular algorithm used for shape registration while conducting inspection during a production process. A crucial key to the success of the ICP is the choice of point selection method. While point selection can be customized for a particular application using its prior knowledge, normal-space sampling (NSS) is commonly used when normal vectors are available. Normal-based approach can be further improved by stability analysis—called covariance sampling. The stability analysis should be accurate to ensure the correctness of covariance sampling. In this paper, we go deep into the details of covariance sampling, and propose a few improvements for stability analysis. We theoretically and experimentally show that these improvements are necessary for further success in covariance sampling. Experimental results show that the proposed method is more efficient and robust for the ICP algorithm.