In this paper we continue the investigation of the SRCEN estimator of the extreme value index $\gamma$ (or the tail index $\alpha=1/\gamma$) proposed in McElroy and Politis (2007) for $\gamma>1/2$. We propose a new estimator based on the local maximum. This, in fact, is a modification of the SRCEN estimator to the case $\gamma>0$. We establish the consistency and asymptotic normality of the newly proposed estimator for i.i.d. data. Also, a short discussion on the comparison of the estimators is included.