  We refine the presentation of the previous paper of our group, Y.Ezawa et
al., Class. Quantum Grav. {\bf 23} (2006), 3205 [arXiv:gr-qc/0507060]. In that
paper, we proposed a canonical formalism of f(R)-type generalized gravity by
using the Lie derivatives instead of the time derivatives. However, the use of
the Lie derivatives was not sufficient. In this note, we make use of the Lie
derivatives as far as possible, so that no time derivatives are used.
