The diagnosability of many interconnection networks under the well-known PMC model and MM* has been examined as a gauge of the multiprocessor systems' diagnosis capacity. The symmetric PMC model (SPMC model), a variation of the famous PMC model, is recently proposed by Zhu et al. Based on the PMC model, the SPMC model is obtained by adding two assumptions: (1) Each pair of neighboring nodes is believed to test each other; (2) For a given syndrome, only its minimal consistent faulty sets are to be located in 1-step diagnosis. As well-known interconnection networks, a number of characteristics of the 3-ary n-cubes have been examined. In this paper, the diagnosability of 3-ary n-cubes under the symmetric PMC model is determined. The result shows that the diagnosability of a 3-ary n-cube under the SPMC model is almost double that of the PMC model.