It is proposed that the Cole-Cole plot method of analysing dielectric data should be replaced by the use of a polarizability plot, in which the imaginary coordinate of the complex function, α(ω) = [epsilon(ω)-1]/[epsilon(ω) + 2], is plotted against its real coordinate. α(ω) is the complex polarizability of a dielectric sphere of unit radius. This quantity is chosen because, in a sphere, long-range dipole-dipole coupling vanishes and therefore α will be a good measure of the intrinsic properties of a substance. This method gives proper weighting to all polarization mechanisms and provides a ready means of comparing the dielectric behaviour of different substances. Because the α-plot is a bilinear transformation of the Cole-Cole plot, circular arcs are transformed into circular arcs and semicircles into semicircles. Experimental results for glycerol, an ethanol-water mixture and for n-propanol are analysed by the new method.