  We describe a framework for constructing the Ricci-flat metrics on the total
space of the canonical bundle over $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$
(the del Pezzo surface of rank one). We construct explicitly the first-order
deformation of the so-called `orthotoric metric' on this manifold. We also show
that the deformation of the corresponding conformal Killing-Yano form does not
exist.
