  We study the relationship between the twisted Orbifold K-theories
${^{\alpha}}K_{orb}(\textsl{X})$ and ${^{\alpha'}}K_{orb}(\textsl{Y})$ for two
different twists $\alpha\in Z^3(G;S^1)$ and $\alpha'\in Z^3(G';S^1)$ of the
Orbifolds $\textsl{X}=[*/G]$ and $\textsl{Y}=[*/G']$ respectively, for $G$ and
$G'$ finite groups. We prove that under suitable hypothesis over the twisting
$\alpha'$ and the group $G'$ we obtain an isomorphism between these twisted
K-theories.
