  Let $(A,\sigma)$ be an Azumaya algebra with an orthogonal involution over a
ring $R$. We prove that if there exists $a\in A$ such that $\sigma(a)a=1$ and
$\operatorname{Nrd}_{A/R}(a)=-1$, then the Brauer class of $A$ is trivial. This
is well-known when $R$ is a field, and was proved recently by the author when
$R$ is semilocal. The proof for general $R$ is very different from the
semilocal case, and does not extend to Azumaya algebras over non-affine
schemes. We also show that at this level of generality, the hypotheses on
$(A,\sigma)$ do not guarantee that $A$ is a matrix algebra over $R$.
