We show that the converse of the aproximation theorem of Andreotti and Grauert does not hold. More precisely we construct a $4$-complete open subset $D\subset {ℂ}^6$ (which is an analytic complement in the unit ball) such that the restriction map $H^3({ℂ}^6,ℱ)\to H^3(D,ℱ)$ has a dense image for every $ℱ\in Coh\left({ℂ}^6\right)$ but the pair $(D,{ℂ}^6)$ is not a $4$-Runge pair.