In inverse problems, redatuming data consists in virtually moving thesensors from the original acquisition location to an arbitrary position. Thisis an essential tool for target oriented inversion. An exact redatumingmethod which has the peculiarity to be robust with respect to noise isproposed. Our iterative method is based on the Time Reversal AbsorbingConditions (TRAC) approach and avoids the need for a regularization strategy. Numerical results and comparisons with other redatumingapproaches illustrate the robustness of our method.