Existing surveys of our galaxy are able to detect CO clouds with an excitation temperature Tex ≳ 5 K. We have made observations to determine if a substantial molecular component is colder than ∼ 5 K. We compared CO emission features with H2CO absorption against 17 continuum sources near the galactic plane. After elimination of features in the spectra that are probably associated with known H II regions, there were 39 clouds remaining, most of which show an excellent kinematic agreement between H2CO and CO. The results do not suggest the existence of a large amount of mass in ultra-cold molecular clouds.