We report magnetic susceptibility performed on overdoped Bi2Sr2CuO6+d powders as a function of oxygen doping d and temperature T. The decrease of the spin susceptibility chis with increasing T is confirmed. At sufficient high temperature, chis presents an unusual linear temperature dependence chis=chis0 -chi1T . Moreover, a linear correlation between chi1 and chis0 for increasing hole concentration has been displayed. These non conventional metal features will be discussed in terms of a singular narrow-band structures.