ON EULER CHARACTERISTIC OF MODULES**

This paper gives a characteristic property of the Euler characteristic for IBN rings. The following results: are proved. （1） If R is a commutative ring, M, N are two stable free R-modules, then χ（MN）=χ（M）χ（N）, where χ denotes the Euler characteristic. （2） If f: K0（R）→Z is a ring isomorphism, where K0（R） denotes the Grothendieck group of R, K0（R） is a ring when R is commutative, then f（[M]）=χ（M） and χ（MN）=χ（M）χ（N） when M, N are finitely generated projective R-modules, where.the isomorphism class [M] is a generator of K0（R）. In addition, some applications of the results above are also obtained.