We have developed a new method that uses wavelet analysis to remove interference fringe patterns from images. This method is particularly useful for flat fields in the common case where fringes vary between the calibration and object data. We analyze the efficacy of this method by creating fake flats with fictitious fringes and removing the fringes. We find that the method removes 90% of the fringe pattern if its amplitude is equal to the random noise level and 60% if the fringe amplitude is ~1/10 of the noise level. We also present examples using real flat-field frames. Version 1.5.5 of a routine written in IDL that implements this algorithm is available from the authors and as an attachment to this paper.