  Detecting galaxies when their star-formation is being quenched is crucial to
understand the mechanisms driving their evolution. We identify for the first
time a sample of quenching galaxies selected just after the interruption of
their star formation by exploiting the [O III]5007/Halpha ratio and searching
for galaxies with undetected [O III]. Using a sample of ~174000 star-forming
galaxies extracted from the SDSS-DR8 at 0.04 < z < 0.21,we identify the ~300
quenching galaxy best candidates with low [O III]/Halpha, out of ~26000
galaxies without [O III] emission. They have masses between 10^9.7 and 10^10.8
Mo, consistently with the corresponding growth of the quiescent population at
these redshifts. Their main properties (i.e. star-formation rate, colours and
metallicities) are comparable to those of the star-forming population,
coherently with the hypothesis of recent quenching, but preferably reside in
higher-density environments.Most candidates have morphologies similar to
star-forming galaxies, suggesting that no morphological transformation has
occurred yet. From a survival analysis we find a low fraction of candidates
(~0.58% of the star-forming population), leading to a short quenching timescale
of tQ~50Myr and an e-folding time for the quenching history of tauQ~90Myr, and
their upper limits of tQ<0.76 Gyr and tauQ<1.5Gyr, assuming as quenching
galaxies 50% of objects without [O III] (~7.5%).Our results are compatible with
a 'rapid' quenching scenario of satellites galaxies due to the final phase of
strangulation or ram-pressure stripping. This approach represents a robust
alternative to methods used so far to select quenched galaxies (e.g. colours,
specific star-formation rate, or post-starburst spectra).
