Let \(\Omega ^+\subset {\mathbb R}^{n+1}\) be a vanishing Reifenberg flat domain such that \(\Omega ^+\) and \(\Omega ^-={\mathbb R}^{n+1}\setminus \overline{\Omega ^+}\) have joint big pieces of chord-arc subdomains and such that the outer unit normal to \(\partial \Omega ^+\) belongs to \({{\text {VMO}}}(\omega ^+)\) , where \(\omega ^\pm \) is the harmonic measure in \(\Omega ^\pm \) . Up to now it was an open question if these conditions imply that \(\log \dfrac{d\omega ^-}{d\omega ^+} \in {{\text {VMO}}}(\omega ^+)\) . In this paper we answer this question in the negative by constructing an appropriate counterexample in \({\mathbb R}^2\) , with the additional property that the outer unit normal to \(\partial \Omega ^+\) is constant \(\omega ^+\) -a.e. in \(\partial \Omega ^+.\)
