The estimation of the extreme value index (EVI) plays a crucial role in modelling and predicting extreme events, such as floods, earthquakes, heatwaves or a financial crisis. The Hill estimator, defined as the average of the log-excesses of a high threshold, is a popular choice for estimating the EVI, primarily due to its simplicity. However, the Hill estimator is known to suffer from bias, particularly when the estimation is based on a large fraction of the sample size. In this paper, we propose a partially bias corrected Hill estimator that addresses this issue and provides more accurate estimates. The performance of the new estimator is illustrated with simulated and real data.