Falk(1994) showed that the asymptotic efficiency of the Pickands estimator of the extreme value index $eta$ can considerably be improved by a simple convex combination. In this paper we propose an alternative estimator of $eta$ which is as asymptotically efficient as the optimal convex combination of the Pickands estimators but has a better finite-sample performance. We prove consistency and asymptotic normality of the proposed estimator. Monte Carlo simulations are conducted to compare the finite-sample performances of the proposed estimator and the optimal convex combination estimator.