$$ \psi \frac{\partial^2 \phi}{\partial x_{\mu} \partial x_{\nu}} -
\begin{Bmatrix}\mu\nu\\\tau\end{Bmatrix} \psi \frac{\partial
\phi}{\partial x_{\tau}} $$
which has a tensor character. Similarly, (∂φ/∂_x__{μ}) (∂φ/∂_x__{ν}) is
also a tensor (outer product of two four-vectors).