  We proposed the discrete Euler top in 2000. In that paper, exact solutions
and conserved quantities are described. However, a Lax pair of our proposed
discrete Euler top is not contained. Moreover, the Lax pair is still unknown.
In this paper, from a generalized eigenvalue problem, we obtain the Lax pair of
the discrete Euler top. In addition, we introduce another Lax pair of the
discrete Euler top in terms of quaternions.
