  This paper deals with a remarkable integrable discretization of the so(3)
Euler top introduced by Hirota and Kimura. Such a discretization leads to an
explicit map, whose integrability has been understood by finding two
independent integrals of motion and a solution in terms of elliptic functions.
Our goal is the construction of its Hamiltonian formulation. After giving a
simplified and streamlined presentation of their results, we provide a
bi-Hamiltonian structure for this discretization, thus proving its
integrability in the standard Liouville-Arnold sense.
