  We have measured the angular correlation of the pair nucleons np and nn
emitted from the nonmesonic weak decay (NMWD) of ^{12}_{Lambda}C produced via
the (pi^+,K^+) reaction in coincidence measurement. The Lambda p -> np and
Lambda n -> 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 N_{nn} and N_{np},
the ratio Gamma_n/Gamma_p of the partial decay widths Gamma_n(Lambda n -> nn)
and Gamma_p(Lambda p -> np) of ^{12}_{Lambda}C was extracted to be
0.51+-0.13(stat) +- 0.05(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 Gamma_n/Gamma_p ratio of
^{12}_{Lambda}C (p-shell) is close to that of ^5_{Lambda}He (s-shell). The
results are consistent with those of recent theoretical calculations.
