The COBE DMR sky maps contain low-level correlated noise. We obtain es
timates of the amplitude and pattern of the correlated noise from thre
e techniques: angular averages of the covariance matrix, Monte Carlo s
imulations of two-point correlation functions, and direct analysis of
the DMR maps. The results from the three methods are mutually consiste
nt. The noise covariance matrix of a DMR sky map is diagonal to an acc
uracy of better than 1%. For a given sky pixel, the dominant noise cov
ariance occurs with the ring of pixels at an angular separation of 60
degrees due to the 60 degrees separation of the DMR horns. The mean co
variance at 60 degrees is 0.45%(+0.18)(-0.14) of the mean variance. Ad
ditionally, the variance in a given pixel is 0.7% greater than would b
e expected from a single beam experiment with the same noise propertie
s. Autocorrelation functions suffer from a similar to 1.5 sigma positi
ve bias at 60 degrees while cross-correlations have no bias. Published
COBE DMR results are not significantly affected by correlated noise.