  The angular power spectrum estimator developed by Peebles (1973) and Hauser &
Peebles (1973) has been modified and applied to the 4 year maps produced by the
COBE DMR. The power spectrum of the observed sky has been compared to the power
spectra of a large number of simulated random skies produced with noise equal
to the observed noise and primordial density fluctuation power spectra of power
law form, with $P(k) \propto k^n$. The best fitting value of the spectral index
in the range of spatial scales corresponding to spherical harmonic indices $3
\leq \ell \lesssim 30$ is an apparent spectral index $n_{app}$ = 1.13 (+0.3)
(-0.4) which is consistent with the Harrison-Zel'dovich primordial spectral
index $n_{pri} = 1$ The best fitting amplitude for $n_{app} = 1$ is $\langle
Q_{RMS}^2\rangle^{0.5}$ = 18 uK.
