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'-> bZ) were obtained for b' masses ranging from 96 to 103 GeV/c(2) stop. These limits, together with the theoretical branching ratios predicted by a sequential four generations model, were used to constrain the value of R-CKM=vertical bar V-cb(') /V-tb'V-tb vertical bar there V-cb', V-tb' and V-tb are elements of the extended CKM matrix.