Blue Compact Dwarf (BCD) galaxies are metal poor systems going through a major starburst that cannot last for long. We have identified galaxies which may be BCDs during quiescence (QBCD), i.e., before the characteristic starburst sets in or when it has faded away. These QBCD galaxies are assumed to be like the BCD host galaxies. The SDSS/DR6 database provides ~21500 QBCD candidates. We also select from SDSS/DR6 a complete sample of BCD galaxies to serve as reference. The properties of these two galaxy sets have been computed and compared. The QBCD candidates are thirty times more abundant than the BCDs, with their luminosity functions being very similar except for the scaling factor, and the expected luminosity dimming associated with the end of the starburst. QBCDs are redder than BCDs, and they have larger HII region based oxygen abundance. QBCDs also have lower surface brightness. The BCD candidates turn out to be the QBCD candidates with the largest specific star formation rate (actually, with the largest H_alpha equivalent width). One out of each three dwarf galaxies in the local universe may be a QBCD. The properties of the selected BCDs and QBCDs are consistent with a single sequence in galactic evolution, with the quiescent phase lasting thirty times longer than the starburst phase. The resulting time-averaged star formation rate is low enough to allow this cadence of BCD -- QBCD phases during the Hubble time. ; Comment: Accepted for publication in ApJ. 17 pages. 13 Figs