  Pursuing the original idea proposed in our previous paper (Paper I), we
improve the method to determine the shape of the initial curvature perturbation
spectrum $P(k)$ from the CMB data. The thickness of the last scattering surface
(LSS) and the integrated Sachs-Wolfe (ISW) effect, which we neglect in Paper I,
are taken into account and an iterative method is newly developed. The new
method can reproduce the primordial power spectra with a high accuracy, given
the correct values of the cosmological parameters. Conversely, there appear
spurious peaks and dips in the reconstructed power spectrum if we use the
cosmological parameters slightly different from the true values, while there
appear regions of negative $P(k)$ in some cases if we use substantially
different values. In other words, the tacit assumption that the cosmological
parameters can be determined for an assumed initial spectrum is verified by our
reconstruction method. In addition, it could be a new tool to constrain the
cosmological parameters without recourse to models of the primordial power
spectra.
