The Rohlin invariant of an oriented closed spin 3-manifold M is
defined to be the signature (mod 16) of an oriented compact spin
4-manifold bounded by M.  The vanishing of the Rohlin invariant of an
amphicheiral integral homology 3-sphere is a consequence of some
elementary properties of the Casson invariant.  
 In this talk we give a new and direct proof of this vanishing
property.  More precisely, we introduce a certain construction of an
oriented compact spin 4-manifold X bounded by M+M+(-M) ('+' denotes
the disjoint union) such that, if M is amphicheiral then the signature
of X vanishes.  The idea of this construction was inspired by the
definition of the degree one part Z_1(M) of the
Kontsevich-Kuperberg-Thurston invariant of M.