  Black holes are found to exist in gravitational theories with the presence of
quadratic curvature terms and behave differently from the Schwarzschild
solution. We present an exhaustive analysis for determining the quasinormal
modes of a test scalar field propagating in a new class of black hole
backgrounds in the case of pure Einstein-Weyl gravity. Our result shows that
the field decay of quasinormal modes in such a non-Schwarzschild black hole
behaves similarly to the Schwarzschild one, but the decay slope becomes much
smoother due to the appearance of the Weyl tensor square in the background
theory. We also analyze the frequencies of the quasinormal modes in order to
characterize the properties of new back holes, and thus, if these modes can be
the source of gravitational waves, the underlying theories may be testable in
future gravitational wave experiments. We briefly comment on the issue of
quantum (in)stability in this theory at linear order.
