  The covariance matrix of random variables $X_1,\dots,X_n$ is said to have an
intraclass covariance structure if the variances of all the $X_i$'s are the
same and all the pairwise covariances of the $X_i$'s are the same. We provide a
possibly surprising characterization of such covariance matrices in the case
when the $X_i$'s are symmetric Bernoulli random variables.
