  In this article it is proved that for every special AJW-algebra $A$ there
exist central projections $e$, $f$, $g\in A$, $e+f+g=1$ such that (1) $eA$ is
reversible and there exists a norm-closed two sided ideal $I$ of $C^*(eA)$ such
that $eA={{}^\perp}(^\perp(I_{sa})_+)_+$; (2) $fA$ is reversible and
$R^*(fA)\cap iR^*(fA)=\{0\}$; (3) $gA$ is a totally nonreversible AJW-algebra.
