  A search for the pair production of fourth generation b'-quarks was performed
using data taken by the DELPHI detector at LEP-II. The analysed data were
collected at centre-of-mass energies ranging from 196 to 209 GeV, corresponding
to an integrated luminosity of 420 pb^{-1}. No evidence for a signal was found.
Upper limits on BR(b' -> bZ) and BR(b' -> cW) were obtained for b' masses
ranging from 96 to 103 GeV/c^2. These limits, together with the theoretical
branching ratios predicted by a sequential four generations model, were used to
constrain the value of R_{CKM}=|V_{cb'}/V_{tb'}V_{tb}|, where V_{cb'}, V_{tb'}
and V_{tb} are elements of the extended CKM matrix.
