  In [7], G. Navarro proposed a refinement of the McKay conjecture involving a
special class of Galois automorphisms. In [6] this new conjecture was verified
by the author for the alternating groups A(n) when p=2. In this note the
Navarro conjecture is verified for the p-singular characters of the principal
block of the alternating groups in the case of abelian defect when p is odd.
