We define an enhanced Brauer category $\wt\CB(m)$ by adding a single generator to the usual Brauer category $\CB(m)$, together with four relations. We then prove that our category $\wt\CB(m)$ is actually equivalent to the category of representations of $\SO_m$ generated by the natural representation. The FFT for $\SO_m$ amounts to the surjectivity of a certain functor $\CF$ on $\Hom$ spaces, while the Second Fundamental Theorem for $\SO_m$ says simply that $\CF$ is injective on $\Hom$ spaces. This theorem provides a diagrammatic means of computing the dimensions of spaces of homomorphisms between tensor modules for $\SO_m$. This is joint work with Gus Lehrer.