  It has been observed earlier that, in principle, it is possible to obtain a
quantum mechanical interpretation of higher order quantum cosmological models
in the spatially homogeneous and isotropic background, if auxiliary variable
required for the Hamiltonian formulation of the theory is chosen properly. It
was suggested that for such a choice, it is required to get rid of all the
total derivative terms from the action containing higher order curvature
invariant terms, prior to the introduction of auxiliary variable. Here, the
earlier work has been modified and it is shown that the action, $A=\beta\int
\sqrt{-g} R^2 d^4 x$ should be supplemented by a boundary term in the form
$\sigma=4\beta\int ^{3}R K \sqrt{h} d^{3}x$, where, $^3 R$, $K$ and $h$ are the
Ricci scalar for three-space, trace of the extrinsic curvature and determinant
of the metric on the three space respectively. The result has been tested in
the background of homogeneous and anisotropic models and thus confirmed.
