Process measurements are contaminated by random and/or gross measuring errors, which degenerates performances of data-based strategies for enhancing process performances, such as online optimization and advanced control. Many approaches have been proposed to reduce the influence of measuring errors, among which expectation maximization (EM) is a novel and parameter-free one proposed recently. In this study, we studied the EM approach in detail and argued that the original EM approach is not feasible to rectify measurements contaminated by persistent biases, which is a pitfall of the original EM approach. So, we propose a modified EM approach here to circumvent this pitfall by fixing the standard deviation of random error mode. The modified EM approach was evaluated by several benchmark cases of process data rectification from literatures. The results show advantages of the proposed approach to the original EM in solving efficiency and performance of data rectification.