  A precise determination of the primordial spectrum of matter density
fluctuations at super-horizon scales is essential in understanding large scale
structure in the universe. Attempts to constrain or obtain the primordial
spectrum using data on cosmic microwave background (CMB) anisotropies has
relied on statistical and correlation analyses that assume a power-law
spectrum. We propose a method to derive $P(k)$ directly from the CMB angular
power spectrum which does not presuppose the need to know anything about its
functional form. The method consists of a direct inversion of the Sachs-Wolfe
formula. Using this new analysis technique and COBE data we obtain an empirical
$P(k)$ which 1) supports a power-law parameterization and 2) has an amplitude
and spectral index consistent with previous analyses of the same data. We
obtained for the spectral index, $n=1.52 \pm 0.4$ when the 2nd year COBE data
is used and $n=1.22 \pm 0.3$ using the 4 year data set.
