Two thermostable levels E(0.31) and E(0.58) related to Rh in Si were observed using deep level transient spectroscopy and double correlation deep level transient spectroscopy techniques. By means of thermal annealing and electron irradiation, the microscopic natures of these levels were identified for the first time. The levels E(0.31) and E(0.58) arise from by the same impurity center but have different charge states. Their microstructures are not related to a pure substitutional Rh atom, but correspond to a complex. This result is compared to our self-consistent theoretical calculation.