Thermodynamical Green's function is investigated for a localized spin system having an alternant character, such as an antiferromagnet and a ferrimagnet, or a paramagnet having an alternant variation in g-factor. It is expressed in terms of spin polarization and the spatial correlations of spin deviations, which are also calculated in the framework of Green's function method. Paramagnetic susceptibility of an antiferro- and a ferri-magnet are discussed using the lowest order solution. Inclusion of the higher order contributions is shown to give an exact spectrum of an antiferromagnet at low temperatures and also to give the resonance width over a whole range of temperature, although it is not so easy to arrive at its final expression at low temperatures.