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The non-commutative torus $C^{*}({\mathbb{Z}}^n,\omega )$ is realized as the $C^{*}$-algebra of sections of a locally trivial $C^{*}$-algebra bundle over $\widehat{S_{\omega }}$ with fibres isomorphic to $C^{*}({\mathbb{Z}}^n/S_{\omega },{\omega }_1)$ for a totally skew multiplier ${\omega }_1$ on ${\mathbb{Z}}^n/S_{\omega }$. D. Poguntke [9] proved that $A_{\omega }$ is stably isomorphic to $C\left(\widehat{S_{\omega }}\right)\otimes C^{*}({\mathbb{Z}}^n/S_{\omega },{\omega }_1)\cong C\left(\widehat{S_{\omega }}\right)\otimes A_{\varphi }\otimes M_{kl}\left(ℂ\right)$ for a simple non-commutative torus $A_{\varphi }$ and an integer $kl$. It is well-known that a stable isomorphism of two separable $C^{*}$-algebras is equivalent to the existence of equivalence bimodule between them. We construct an $A_{\omega }$-$C\left(\widehat{S_{\omega }}\right)\otimes A_{\varphi }$-equivalence bimodule.