  Let $E$ be a uniform bundle on an arbitrary generalised Grassmannian $X$
defined over $\mathbb{C}$. We show that if the rank of $E$ is at most
$e.d.(\mathrm{VMRT})$, then $E$ necessarily splits. For some generalised
Grassmannians, we prove that the upper bounds $e.d.(\mathrm{VMRT})$ are optimal
and classify all unsplit uniform bundles of minimal ranks.
