The local magnitude scale M_L is defined by the difference between the observed amplitude (\(\log A\)) and the anchored attenuation amplitude (\(\log A_{0}\)). A previous study in Taiwan established a model of the anchored amplitude as a function of the hypocentral distance R by matching the M_L to the corresponding moment magnitude M_W. Although the overall performance of the model is adequate, there remain some drawbacks, namely, the correlated empirical station correction problem and relatively low sample size. In this paper, we adopt the concept of the expectation-maximization (EM) algorithm to develop a new method that can simultaneously estimate the anchored amplitude model coefficients and station corrections. The revised catalog using the latest dataset in Taiwan provides an up-to-date accurate estimate of M_L. Additionally, the proposed method can systematically obtain statistically meaningful results and be applied to datasets of other regions in the future.