  Via a natural degeneration of Grassmannian manifolds $G(k,n)$ to Gorenstein
toric Fano varieties $P(k,n)$ with conifold singularities, we suggest an
approach to study the relation between the tautological system on $G(k,n)$ and
the extended GKZ system on the small resolution $\hat{P}(k,n)$ of $P(k,n)$. We
carry out the simplest case $(k,n)=(2,4)$ to ensure its validity and show that
the extended GKZ system can be regarded as a tautological system on
$\hat{P}(2,4)$.
