Heavy-tailed distribution can well explain the economic, natural and social phenomena such as asset prices, income
 distribution, hydro-geology, social media, etc.
 Accurate estimation of extreme value index is a key technique for application of heavy-tailed
 distribution. The Hill estimator, introduced in 1975, which opened a precedent of estimating extreme value index, is still
 the focus of heavy-tailed modeling up to now. In order to overcome the shortcomings of the location variation and
 asymptotic behavior of the existing estimators, borrowing the asymptotic expansion of statistic $M_{n}^{(\alpha)}(k_{0},k)$,
  this paper proposes a new kind of location invariant extreme value index estimator (NLIE) and studies its asymptotic expansion under second order regular variation. The optimal choice of threshold is discussed as well. The NLIE is compared with the classical location invariant estimator $\hat{\gamma}_{n}^{H}(k_{0},k)$ by Monte-Carlo. The results show that NlIE behaves better than $\hat{\gamma}_{n}^{H}(k_{0},k)$.