Let $X$ be a scheme, let $\mathcal{A}$ be a sheaf of locally free algebras on $X$. We say $\mathcal{A}$ is an azumaya algebra, if the natural map $$\mathcal{A}\otimes_{\mathcal{O}_X}\mathcal{A}^{opp}\to\mathcal{E}nd_{\mathcal{O}_X}(\mathcal{A}), $$ $$a\otimes b\mapsto (x\mapsto axb)$$ is an isomorphism.

Two azumaya algebras $\mathcal{A},\mathcal{B}$ are called Morita equivalent, if there exists locally free sheaves $\mathcal{F},\mathcal{G}$, such that $$\mathcal{A}\otimes\mathcal{E}nd_{\mathcal{O}_X}(\mathcal{F})\cong\mathcal{B}\otimes\mathcal{E}nd_{\mathcal{O}_X}(\mathcal{G}).$$

Let $\mathcal{A}$ be an Azumaya algebra, which is Morita equivalent to $\mathcal{B}:=\mathcal{O}_X$, does $\mathcal{A}$ necessarily have the form $\mathcal{E}nd_{\mathcal{O}_X}(\mathcal{H})$ for some locally free sheaf $\mathcal{H}$ on $X$?