  In the present paper we construct two new explicit complex bordisms between
any two projective bundles over $\mathbb{C} P^1$ of the same complex dimension,
including the Milnor hypersurface $H_{1,n}$ and $\mathbb{C} P^1\times
\mathbb{C} P^{n-1}$. These constructions reduce the bordism problem to the
null-bordism of some projective bundle over $\mathbb{C} P^1$ with the
non-standard stably complex structure.
