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We have investigated a possible scheme to reduce 1/f noise generated by thermally activated hopping of vortices in SQUIDs by trying to remove vortices from the SQUID body, or at least move them to pinning sites having a high pinning energy. This is accomplished by a "demagnetisation" scheme using a high frequency magnetic field. Niobium SQUIDs were carefully cooled in a magnetically well shielded environment and then exposed to switching transients. The thereby generated low frequency excess noise or an increased white noise could substantially be reduced by this demagnetisation process. The temperature dependence of the flux signal of the flux locked SQUID and the magnetic field dependence of this drift could also be reduced in cases where the drift was caused by motion of trapped vortices. The influence of frequency and amplitude of the demagnetisation field on the amount of noise reduction was studied in some detail.