Let \(t_ n\) be the estimator of the parameter \(\theta\) such that the following asymptotic expansion takes place \[ E_{\theta}t_ n=\theta +a_ 1(\theta)/b(n)+a_ 2(\theta)/b^ 2(n)+... \] Here \(a_ i(.)\), \(i=1,2,..\). are unknown, and b(n)\(\to \infty\) as \(n\to \infty\). The author shows how to construct new estimators \(t^*_ n\) based on \(t_ n\) such that \(E_{\theta}t^*_ n=\theta +a^*_ 2(\theta)/b^ 2(n)+...\) It is stated that a similar approach can be used to improve the asymptotic properties of the well-known nonparametric Parzen density estimators.