The infrared spectra of the carbon monoxide-water cluster as well as the CO monomer and dimer in an argon matrix at cryogenic temperatures have been reinvestigated on the basis of the isotope substitution experiment with (CO)-C-12 and (CO)-C-13. Lines due to the CO-H2O 2-1 cluster in the matrix have been unambiguously identified in the CO and OH stretching regions. The isotope effect on the vibrational frequency of the cluster is observed in the CO stretching vibration but neither in the symmetric nor antisymmetric OH stretching vibrations. Each of the two vibrational lines due to the two CO vibrations of the CO-H2O 2-1 cluster is examined by comparing the expected spectral features at a (CO)-C-12/(CO)-C-13 ratio on a simulation with those observed experimentally. The migration of the trapped molecules (CO and H2O) in the matrix is discussed, in which the observed spectral change with the deposition temperature from 14 K to 30 K is explained. (C) 2004 American Institute of Physics.