The charged lepton flavor violation (CLFV) is a good probe to search for new physics beyond the standard model. Though various CLFV processes have been investigated, any singns of new physics have not yet found. In 2010, the CLFV decay of the muonic atom, μ- e- → e- e-, was proposed as one of the promising processes. In this talk, I report on our improved analysis of this process by taking into account the distortion of the out-going electrons in the nuclear Coulomb potential and the relativistic treatment of the muon and the electrons. These effects are important and modify the previous understanding of the mass number dependence of transition rate. I also talk that the process has a capability to discriminate between contact and photonic CLFV interactions.