Generalized estimating equations produce consistent estimators of the mean parameters for spatially correlated binary data, but the estimation of covariance matrix is also of interest in spatial data analysis. In this talk, a specific parametric form is proposed to model the correlation matrix for spatially correlated binary data. An iterative approach based on generalized estimating equations is developed to estimate the mean and correlation parameters simultaneously. Asymptotic properties including consistency and normality of the estimators of the mean and correlation parameters are considered. Simulation studies are conducted through considering various model parameters such as different working correlation matrices, correlation parameters and dimensions of the mean parameters. The proposed approach is applied to the analysis for the spatial bovine tuberculosis infection data in Ireland, aiming to measure the influence of important factors on the infection for both badgers and cattle, by taking into account the correlations between their setts and herds.