The sample variance of a tally in Monte Carlo eigenvalue calculations is biased because of an intercycle correlation between the fission source distributions (FSDs). How to estimate the variance bias or equivalently how to calculate the real variance has been an interesting subject of study. This paper proposes a new method to estimate the real variance based on an intercycle covariance of the FSDs that can be derived from the cycle-by-cycle stochastic error propagation model. The proposed method enables one to calculate every intercycle covariance of a tally accurately, regardless of the number of active cycles. Therefore, the method can be applied satisfactorily even to problems with the dominance ratio (DR) close to 1. The accuracy of the new method is examined for small- and medium-sized pressurized water reactor core problems and a fuel storage facility problem exhibiting a slow source convergence. It is shown that the new method is capable of predicting the variance bias strikingly better than the existing methods, especially for problems with high DRs.