We report on the results of our detailed analyses on the peculiar recombining plasma of the supernova remnant (SNR) G359.1$-$0.5, and the interacting CO clouds. Combining {it Chandra} and {it Suzaku} data, we estimated the ionization state of the plasma with a careful treatment of the background spectrum. The average spectrum showed a remarkably large deviation of the electron temperature ($sim$0.17 keV) from the initial temperature ($>$ 16 keV), indicating that the plasma is in a highly recombination-dominant state. On the other hand, the recombination timescale $({it n_{rm e} t})$ is comparable to those of the other recombining SNRs ($sim4.2 times 10^{11}$ 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 $sim -$20 km s$^{-1}$. This indicates that the SNR is located at a distance of $sim$4 kpc, which is the foreground of the Galactic center, as previously reported. The associated CO cloud does not show clear spatial coincidence with the nearby GeV/TeV emission, indicating that the origins of the GeV/TeV emission are likely unrelated to G359.1$-$0.5.
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