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Let $c,h$ and $c,\tilde{h}$ be two admissible pairs of central charge andhighest weight for ${\rm Diff}^+(S^1)$. It is shown here that the positiveenergy irreducible projective unitary representations $U_{c,h}$ and$U_{c,\tilde{h}}$ of the group ${\rm Diff}^+(S^1)$ are locally equivalent. Thismeans that for any $I\Subset S^1$ open proper interval, there exists a unitaryoperator $W_I$ such that $W_I U_{c,h}(\gamma)W_I^* = U_{c,\tilde{h}}(\gamma)$for all $\gamma \in {\rm Diff}^+(S^1)$ which act identically on $I^c\equivS^1\setminus I$ (i.e. which can "displace" or "move" points only in $I$). Thisresult extends and completes earlier ones that dealt with only certain regionsof the "$c,h$-plane", and closes the gap in the full classification ofsuperselection sectors of Virasoro nets.

Local equivalence of representations of Diff$^+(S^1)$ corresponding to different highest weights