  When the cohomology ring of a generalized Bott manifold with
$\mathbb{Q}$-coefficient is isomorphic to that of a product of complex
projective spaces $\mathbb{C}P^{n_i}$, the generalized Bott manifold is said to
be $\mathbb{Q}$-trivial. We find a necessary and sufficient condition for a
generalized Bott manifold to be $\mathbb{Q}$-trivial. In particular, every
$\mathbb{Q}$-trivial generalized Bott manifold is diffeomorphic to a
$\prod_{n_i>1}\mathbb{C}P^{n_i}$-bundle over a $\mathbb{Q}$-trivial Bott
manifold.
