Is the following a valid combinatorial proof of the Stirling identity?

Prove S(n,n-1) = $\displaystyle \left({n\atop 2}\right)$.

First look at the partition of n into n blocks. We then have blocks $\displaystyle n_{1},n_{2},...,n_{n}$. Now if we partition n into n-1 blocks, some $\displaystyle n_{i},n_{j}$ will have to share a block. This is the same as choosing 2 from n.