The noncommutative torus $C^*(\mathbb Z^n,\,\omega)$ of rank $n$ is realized as the
$C^*$-algebra of sections of a locally trivial continuous
$C^*$-algebra bundle over $\widehat{S_{\omega}}$ with fibres
$C^*(\mathbb Z^n/S_{\omega},\, \omega_1)$ for some totally skew
multiplier $\omega_1$ on $\mathbb Z^n/S_{\omega}$. It is shown that
$C^*(\mathbb Z^n/S_{\omega},\,\omega_1)$ is isomorphic to
$A_{\varphi}\otimes M_k(\mathbb C)$ for some completely irrational
noncommutative torus $A_{\varphi}$ and some positive integer $k$, and that
$A_{\omega} \otimes M_{l^{\infty}}$ has the trivial bundle structure if and
only if the set of prime factors of $k$ is a subset of the set of prime
factors of $l$. This is applied to understand the bundle structure of the tensor
products of Cuntz algebras with noncommutative tori.