  We review and elaborate on some aspects of the classically scale-invariant
renormalizable 4-derivative scalar theory $L= \phi\, \partial^4 \phi + g
(\partial \phi)^4$. Similar models appear, e.g., in the context of conformal
supergravity or in the description of the crystalline phase of membranes.
Considering this theory in Minkowski signature we suggest how to define
Poincare-invariant scattering amplitudes by assuming that only massless
oscillating (non-growing) modes appear as external states. In such
shift-symmetric interacting theory there are no IR divergences despite the
presence of $1/q^4$ internal propagators. We discuss how non-unitarity of this
theory manifests itself at the level of the one-loop massless scattering
amplitude.
