  We report the discovery of a high CO(J=3-2)/CO(J=1-0) ratio gas with an
arc-like distribution (``high-ratio gas arc'') surrounding the central star
cluster of the supergiant HII region NGC 604 in the nearby spiral galaxy M 33,
based on multi-J CO observations of a 5' $\times$ 5' region of NGC 604
conducted using the ASTE 10-m and NRO 45-m telescopes. The discovered
``high-ratio gas arc'' extends to the south-east to north-west direction with a
size of $\sim$ 200 pc. The western part of the high-ratio gas arc closely
coincides well with the shells of the HII regions traced by H$\alpha$ and radio
continuum peaks. The CO(J=3-2)/CO(J=1-0) ratio, R_{3-2/1-0}, ranges between 0.3
and 1.2 in the observed region, and the R_{3-2/1-0} values of the high-ratio
gas arc are around or higher than unity, indicating very warm (T_kin > 60 K)
and dense (n(H_2) > 10^{3-4} cm^{-3}) conditions of the high-ratio gas arc. We
suggest that the dense gas formation and second-generation star formation occur
in the surrounding gas compressed by the stellar wind and/or supernova of the
first-generation stars of NGC 604, i.e., the central star cluster of NGC 604.
