Raman Spectroscopy is a widely used analytical technique, favoured when molecular specificity with minimal sample preparation is required.<br>The majority of Raman instruments use charge-coupled device (CCD) detectors, these are susceptible to cosmic rays and as such multiple spurious spikes can occur in the measurement. These spikes are problematic as they may hinder subsequent analysis, particularly if multivariate data analysis is required. In this work we present a new algorithm to remove these spikes from spectra after acquisition. Specifically we use calculation of modified <i>Z</i> scores to locate spikes followed by a simple moving average filter to remove them. The algorithm is very simple and its execution is essentially instantaneous, resulting in spike-free spectra with minimal distortion of actual Raman data. The presented algorithm represents an improvement on existing spike removal methods by utilising simple, easy to understand mathematical concepts, making it ideal for experts and non-experts alike. <br>