  We discuss the proposal of a new method to transform a f(R) metric gravity
theory into a general relativistic theory including an auxiliary scalar field,
recently introduced by S. Cotsakis et al. We argue that (i) the fact that the
fourth order equations of f(R) metric gravity can be recast (via a Legendre
transformation) into Einstein equations without any conformal rescaling has
been thoroughly clarified in the previous literature, and (ii) the newly
proposed method produces a set of equations that are not equivalent to the
original theory. In the conclusion, a comment is added on another aspect of the
Legendre transformation which seems to be generally overlooked.
