There are still challenges when meta-analyzing data from studies on diagnostic accuracy. This is mainly due to the bivariate nature of the response where information on sensitivity and specificity must be summarized while accounting for their correlation within a single trial. In this paper, we propose a new statistical model for the meta-analysis for diagnostic accuracy studies. This model uses beta-binomial distributions for the marginal numbers of true positives and true negatives and links these margins by a bivariate copula distribution. The new model comes with all the features of the current standard model, a bivariate logistic regression model with random effects, but has the additional advantages of a closed likelihood function and a larger flexibility for the correlation structure of sensitivity and specificity. In a simulation study, which compares three copula models and two implementations of the standard model, the Plackett and the Gauss copula do rarely perform worse but frequently better than the standard model. We use an example from a meta-analysis to judge the diagnostic accuracy of telomerase (a urinary tumor marker) for the diagnosis of primary bladder cancer for illustration. Copyright © 2013 John Wiley & Sons, Ltd.