The conventional formula for estimating the extended Gini coefficient is a covariance formula provided by Lerman and Yitzhaki (1989). We suggest an alternative estimator, obtained by approximating the Lorenz curve by a series of linear segments. In a Monte Carlo experiment designed to assess the relative bias and efficiency of the two estimators, we find that, when using grouped data with 20 or fewer groups, our new estimator has less bias and lower mean squared error than the covariance estimator. When individual observations are used, or the number of groups is 30 or more, there is little or no difference in the performance of the two estimators.