  We discuss the properties of scattering amplitudes in a conformal bi-scalar
fishnet theory that previously appeared in the study of integrable deformations
of $\mathcal N=4$ SYM. In distinction with the latter theory, the scattering
amplitudes in the conformal fishnet theory do not suffer from infrared
divergences and possess enhanced symmetries. We demonstrate that for the
simplest four-particle scattering the single- and double-trace partial
amplitudes can be computed for arbitrary coupling in the leading color
approximation. We also review the invariance of single-trace components of
multi-particle fishnet amplitudes in the leading color limit under
infinite-dimensional Yangian symmetry.
