  In this paper we show the lower bound of the set of non-zero $-K^2$ for
normal surface singularities establishing that this set has no accumulation
points from above. We also prove that every accumulation point from below is a
rational number and every positive integer is an accumulation point. Every
rational number can be an accumulation point modulo $\bZ$. We determine all
accumulation points in $[0, 1]$. If we fix the value $-K^2$, then the values of
$p_g$, $p_a$, mult, embdim and the numerical indices are bounded, while the
numbers of the exceptional curves are not bounded.
