We consider bias-corrected estimation of the extreme value index of a Pareto-type distribution in the censoring framework. The initial estimator is based on a Kaplan-Meier integral from which we remove the bias under a second-order framework. This estimator depends on a suitable external estimation of second-order parameters which is also discussed. The weak convergence of the bias-corrected estimator is established. It has the nice property to have the same asymptotic variance as the initial estimator. This nice feature is illustrated on a simulation study where our estimator is compared to alternatives already introduced in the literature. Finally, our methodology is applied on an insurance dataset.