The thermoelectric power S(T) of single-layer Bi2Sr2CuO6+d is studied as a function of oxygen doping in the strongly overdoped region of the phase diagram (T, d). As other physical properties in this region, diffusion thermopower Sdiff(T) also shows an important deviation from conventional Fermi liquid behaviour. This departure from T-linear S(T) dependence together with the results of susceptibility on the same samples suggest that the origin of the observed non-metallic behaviour is the existence of a singularity in the density of states near the Fermi level. The doping and temperature dependence of themopower is compared with a tight-binding band model.