  We give a counterexample to the Kawauchi conjecture on the Conway polynomial
of achiral knots which asserts that the Conway polynomial $C(z)$ of an achiral
knot satisfies the splitting property $C(z)=F(z)F(-z)$ for a polynomial $F(z)$
with integer coefficients. We show that the Bonahon-Siebenmann decomposition of
an achiral and alternating knot is reflected in the Conway polynomial. More
explicitly, the Kawauchi conjecture is true for quasi-arborescent knots and
counterexamples in the class of alternating knots must be quasi-polyhedral.
