We report on the results of our detailed analyses on the peculiar recombining plasma of the supernova remnant (SNR) G359.1−0.5, and the interacting CO clouds. Combining Chandra and Suzaku data, we estimated the ionization state of the plasma with a careful treatment of the background spectrum. The average spectrum showed a remarkably large deviation of the electron temperature (∼0.17 keV) from the initial temperature (> 16 keV), indicating that the plasma is in a highly recombinationdominant state. On the other hand, the recombination timescale (n e t) is comparable to those of the other recombining SNRs (∼ 4.2 × 10 11 cm −3 s). We also searched for spatial variation of the plasma parameters, but found no significant differences.Using 12 CO(J=2-1) data obtained with NANTEN2, we found a new, plausible candidate for the interacting CO cloud, which has a line-of-sight velocity of ∼ −20 km s −1 . This indicates that the SNR is located at a distance of ∼4 kpc, which is the foreground of the Galactic center, as previously reported. The associated CO cloud does not show clear spatial coincidence with the nearby GeV/TeV emission, indicating that the origins of the GeV/TeV emission are likely unrelated to G359.1−0.5.