Abstract: We investigate estimators for the covariance matrix of the correlogram of a time series modeled by a stationary Gaussian random process. It is shown that the formulas proposed in publications yield a large bias, which in the general case is comparable to the estimated quantities. We have constructed an unbiased estimator for the full covariance matrix of the correlogram, which does not require asymptotics of a large number of observations N → ∞ or assumptions regarding the behavior of the correlation function of the random process. The transition to an unbiased estimator does not lead to an increase in its error; on the contrary, in numerical tests the variance of the classical estimator turned out to be larger than that of the unbiased one. The practical application of the unbiased estimator is currently limited by the computational complexity of the problem, because it requires the inversion of N2 × N2 matrices, which without the use of specialized algorithms is feasible only up to N ~ 300.