The spin angular momentum (AM) of a light beam appears due to presence of circular or elliptic polarization. Its characterization is coupled with some paradoxical features which are commonly recognized but, to our opinion, are not satisfactorily explained in the known literature. Namely, for a spatially-homogeneous circularly polarized beam, the spin AM density is zero at every point of the beam's cross section while the beam itself carries the non-zero AM. We discuss the physical reasons of this situation. Like the orbital AM, the spin one originates from the transverse energy circulation but here this circulation takes place within microscopic cells whose sizes theoretically tend to zero. In the middle of the beam cross-section adjacent cells compensate each other and the macroscopic circulation vanishes. The compensation disappears if the cells differ (inhomogeneous beam) or if the cell series breaks. The latter situation occurs not only at a real beam boundary but also when a limited part of the beam cross-section is isolated, e.g., by an absorbing object. A correct way for calculating the spin AM of a transversely limited part of an optical beam must take into account, in addition to the common "volume" contribution, also the "boundary" part. Corresponding corrected formula for the spin AM is derived that allows to remove the mentioned paradox and substantiates the usual representation for the volume density ofthe spin AM.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.