The fundamental motivation to study the non-mesonic weak decay (NMWD) of Λ hypernuclei is that it provides the unique channel for the information of the baryon-baryon weak interaction in SU3f group. The relative strength of the two main channels of NMWD whose decay processes are the Λp → np and Λn → nn has been the long standing puzzle during last several decades. The puzzling status has been settled down recently with the Γn/Γp value converging to ~0.5. The large experimental values of Γn/Γp of the previous measurements turned out to be due to the surprisingly large contribution of the competing three-body NMWD, ΛNN → nNN process. This paper discusses about the first measurement of the branching ratio of the three-body NMWD process and the renormalized intra-nuclear cascade method adopted to disentangle the contribution of the three-body process out of those due to final state interaction. And the prospects of the more accurate measurement of the three-body process also are presented.