The star formation history in galaxies is one of the most important parameters to constrain cosmological models, the formation and evolution of galaxies and star formation theories. In this paper we develop a non-parametric method to estimate the star formation history of a galaxy from its spectrum. We use the stellar population synthesis algorithm BC2001 [1], chi(2) minimization techniques and standard statistical methods to measure the confidence levels in the recovered star formation history. In order to study the efficacy of the method we simulate synthetic spectra with different known star formation histories using BC2001, and we succesfully recover all of them.