  In this paper we give a criterion for an isolated, hypersurface singularity
of dimension $n\ (\geq 2)$ to have the canonical modification by means of a
suitable weighted blow-up. Then we give a counter example to the following
conjecture by Reid-Watanabe: For a 3-dimensional, isolated, non-canonical,
log-canonical singularity $(X,x)$ of embedded dimension 4, there exists an
embedding $(X,x)\subset ({\bC}^4, 0)$ and a weight ${\bw}=(w_0,w_1,\ldots
,w_n)$, such that the ${\bw}$-blow-up gives the canonical modification of
$(X,x)$.
