  The rank $n$ swapping algebra is the Poisson algebra defined on the ordered
pairs of points on a circle using the linking numbers, where a subspace of
$(\mathbb{K}^n \times \mathbb{K}^{n*})^r/\operatorname{GL}(n,\mathbb{K})$ is
its geometric mode. In this paper, we find an injective Poisson homomorphism
from the Poisson algebra on Grassmannian $G_{n,r}$ arising from boundary
measurement map to the rank $n$ swapping fraction algebra.
