  In this paper, we consider the asymptotic behavior of positive solutions of
the biharmonic equation $$ \Delta^2 u = u^p~~~~~~~in ~ B_1 \backslash \{0\}$$
with an isolated singularity, where the punctured ball $B_1 \backslash \{0\}
\subset \mathbb{R}^n$ with $n\geq 5$ and $\frac{n}{n-4} < p < \frac{n+4}{n-4}$.
This equation is relevant for the $Q$-curvature problem in conformal geometry.
We classify isolated singularities of positive solutions and describe the
asymptotic behavior of positive singular solutions without the sign assumption
for $-\Delta u$. We also give a new method to prove removable singularity
theorem for nonlinear higher order equations.
