A modified algorithm of the numerical calculation of adiabatic corrections is proposed. It is based on earlier approaches, introduced by Cencek and Kutzelnigg and by the present author. The adiabatic correction is approximated in terms of overlap integrals between electronic wave functions for a given geometry and for a single nucleus shifted by h. The leading term of error is proportional to the square of h in the original methods. The new approach, while requires the same wave functions as those methods, shrinks the error, so that it becomes proportional to h4 in atomic cases. Test calculations show, that similar behavior is retained also for two–atom molecules and additional stable decimal digit of the adiabatic correction can be obtained.