We present a method to select galaxies in the critical phase when the star formation is rapidly suppressed (‘Quenching’). These objects were spectroscopically searched, in the local Universe (0.04 ≤ z < 0.21), by exploiting the dust-corrected [OIII]λ5007/Hα ratio that is quite sensitive to the ionization parameter. We identified roughly 300 quenching candidates amongst 174000 SDSS star-forming galaxies. We analysed their fundamental properties (such SFR, colours, mass) and the Quenching timescale and we found that they stopped the star formation no more than a few Myrs before. Therefore, they can give precise information about the mechanism driving the Quenching, in particular, the role of galaxy mass and halo mass, the role of environment and the role of stars and AGN feedback.