The present paper suggests a new algorithm for estimation of peak positions in FTMS spectra. It is shown theoretically and experimentally that the new technique yields superior results compared to the currently applied techniques, when the noise level is high and/or the peaks are located close to each other. Cases are presented where the deviation from the true mass could be mistaken for space charge effect, while the shift is in fact solely due to the shortcomings of the current techniques and can be corrected by applying the shifted-basis technique. In two out of three cases, this technique gave more accurate (>5 times) result compared to the conventional analysis. In the third case, where the signal was high compared to the noise, the results were comparable. The new technique can be used to achieve better mass accuracy for noisy and not well resolved spectra, and to further investigate the features of the space charge effect.