  In this paper, we construct a local ring $A$ such that the kernel of the map
$G_0(A)\subq \to G_0(\hat{A})\subq$ is not zero, where $\hat{A}$ is the
comletion of $A$ with respect to the maximal ideal, and $G_0()\subq$ is the
Grothendieck group of finitely generated modules with rational coefficient. In
our example, $A$ is a two-dimensional local ring which is essentially of finite
type over ${\Bbb C}$, but it is not normal.
