  Let A be a simple unital AT algebra of real rank zero and Inn(A) the group of
inner automorphisms of A. In the previous paper we have shown that the natural
map of the group of approximately inner automorphisms into Ext(K_1(A),K_0(A))
oplus Ext(K_0(A),K_1(A)) is surjective; the kernel of this map includes the
subgroup of automorphisms which are homotopic to Inn(A). In this paper we
consider the quotient of the group of approximately inner automorphisms by the
smaller normal subgroup AInn(A) which consists of asymptotically inner
automorphisms and describe it as OrderExt(K_1(A),K_0(A)) oplus
Ext(K_0(A),K_1(A)), where OrderExt(K_1(A),K_0(A)) is a kind of extension group
which takes into account the fact that K_0(A) is an ordered group and has the
usual Ext as a quotient.
