  Given a connection $A$ on a $SU(2)$-bundle $P$ over $\mathbb{R}^4$ with
finite Yang-Mills energy $YM(A)$ and nonzero curvature $F_A(0)$ at the origin,
and given $\rho>0$ small enough, we construct a new connection $\hat A$ on a
bundle $\hat P$ of different Chern class ($|c_2(A)-c_2(\hat A)|=8\pi^2$), in
such a way that $\hat A$ is gauge equivalent to $A$ in $\mathbb{R}^4\setminus
B_\rho(0)$ and $$YM(\hat A)\le YM(A)+8\pi^2-\varepsilon_0\rho^4|F_A(0)|^2$$ for
a universal constant $\varepsilon_0>0$.
