We have measured the angular correlation of the pair nucleons np and nn emitted from the nonmesonic weak decay (NMWD) of Λ 12C produced via the (π+,K+) reaction in coincidence measurement. The Λp → np and Λn → nn modes were clearly identified by measuring the back-to-back correlation of the emitted nucleon pairs which is the characteristic of two-body kinematics. From the measured nucleon pair numbers Nnn and Nnp, the ratio Γn/Γp of the partial decay widths Γn(Λn → nn) and Γp(Λp → np) of Λ12C was extracted to be 0.51 ± 0.13(stat)±0.04(syst); this result is almost free from the ambiguity due to the nuclear final state interaction and 3-body decay process, which were inherent in the previous results. The obtained Γn/ Γp ratio of Λ12C (p-shell) is close to that of Λ5He (s-shell). The results are consistent with those of recent theoretical calculations.