For any ordinal number \(\alpha\), let \(H_{\alpha}\) be the set of ordinal numbers less than \(\omega^{\alpha}\). The \(\alpha\)-bicyclic semigroup is \(H_{\alpha}\times H_{\alpha}\) with the operation \[ (\beta,\gamma)(\delta,\eta)=(\beta +(\max (\gamma,\delta)-\gamma,\quad \eta +(\max (\gamma,\delta)-\delta), \] where \(+\) is ordinal addition. It is known that this semigroup cannot have a locally compact topology for which it becomes a topological inverse semigroup, other than the discrete topology. In this paper it is shown, by putting \(\alpha =2\), that this result is untrue if we do not restrict ourselves to locally compact topologies.