We propose a simple method to minimize the residual environmental influence which may exist in paleointensity records obtained from sediments. It consists of adding, or subtracting, a fraction of the normalizer ($kappa$, ARM, or IRM) to the normalized intensity record, so that the corrected record exhibits fluctuations uncorrelated with those of the normalizer. This method was tested with paleointensity records obtained from two cores taken at midlatitude in the South Indian Ocean cores, eastward of the Kerguelen plateau. For each core, correction increases the correlation between the three normalized intensity records, NRM/$kappa$, NRM/ARM, and NRM/IRM. It also reduces the coherence between paleointensity records and bulk magnetic parameters used as normalizers. Although it has to be used with caution, this correction may improve paleointensity records by reducing nongeomagnetic influence. It can also be used to detect intervals where paleointensity may be unreliable, i.e., intervals where large differences between uncorrected and corrected records are observed, before and after correction.