Similarity of quadratic forms over global fields in characteristic 2

Let $K$ be a global function field of characteristic $2$. For each non-trivial place $v$ of $K$, let $K_v$ be the completion of $K$ at $v$. We show that if two non-degenerate quadratic forms are similar over every $K_v$, then they are similar over $K$. This provides an analogue of the version for characteristic not $2$ previously obtained by T.Ono.