We measured infrared absorption spectra of crystalline II of CH4 and succeeded in detecting a prominent Q(2) peak in the ν3 vibrational region by rapid cooling after annealing as well as previously reported rovibrational and librational-vibrational peaks. The integral intensities of the R(0), R(1), and Q(2) peaks were found to show biexponential dependence on time. This clearly demonstrates the interconversion among the three nuclear-spin isomers occupying low-lying rotational levels. The two relaxation rates obtained by biexponential fitting were (0.48, 2.3), (1.1, 4.1), (2.3, 5.1), and (3.4, 15.3) in units of inverse hour (h-1) at 5.2, 6.0, 6.5, and 7.0 K, respectively.