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Pursuing the original idea proposed in our previous paper (Paper I), weimprove the method to determine the shape of the initial curvature perturbationspectrum $P(k)$ 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 newmethod can reproduce the primordial power spectra with a high accuracy, giventhe correct values of the cosmological parameters. Conversely, there appearspurious peaks and dips in the reconstructed power spectrum if we use thecosmological parameters slightly different from the true values, while thereappear regions of negative $P(k)$ in some cases if we use substantiallydifferent values. In other words, the tacit assumption that the cosmologicalparameters can be determined for an assumed initial spectrum is verified by ourreconstruction method. In addition, it could be a new tool to constrain thecosmological parameters without recourse to models of the primordial powerspectra.Comment: 9 pages, 4 figures. Accepted for publication in JCA

Cosmic inversion: II. An iterative method for reproducing the primordial spectrum from the CMB data