Functional Near Infrared Spectroscopy (fNIRS) enables researchers to conduct studies in situations where use of other functional imaging methods is impossible. An important shortcoming of fNIRS is the sensitivity to motion artifacts. We propose a new wavelet based algorithm for removing movement artifacts from fNIRS signals. We tested the method on simulated and experimental fNIRS data. The results show an average of 18.97dB and 15.54dB attenuation in motion artifacts power for our two test subjects without introducing significant distortion in the artifact-free regions of the signal.