  Method: Measuring excitation functions for $^{6}$He+$\alpha$ scattering,
populating states in the excitation energy range from 4.5 MeV to 8 MeV in
$^{10}$Be using a $^6$He rare-isotope beam and a thick helium gas target.
Results: No new excited states in $^{10}$Be have been observed. Stringent
limitation on the possible degree of $\alpha$-clustering of the hypothetical
yrast 6$^+$ state has been obtained. Conclusions: The high-spin members of the
$\alpha$:2n:$\alpha$ molecular-like rotational band configuration, that is
considered to have a 0$^+$ bandhead at 6.18 MeV, either do not exist or have
small overlap with the $^{6}$He(g.s.)+$\alpha$ channel.
