In this paper we study the energy of ULF electromagnetic waves that were recorded by the satellite DEMETER, during its passing over Haiti before and after a destructive earthquake. This earthquake occurred on 12 January 2010, at geographic Latitude 18.46° and Longitude 287.47°, with Magnitude 7.0 R. Specifically, we are focusing on the variations of energy of Ez-electric field component concerning a time period of 100 days before and 50 days after the strong earthquake. In order to study these variations, we have developed a novel method that can be divided in two stages: first we filter the signal, keeping only the ultra low frequencies and afterwards we eliminate its trend using techniques of Singular Spectrum Analysis (SSA), combined with a third-degree polynomial filter. As it is shown, a significant increase in energy is observed for the time interval of 30 days before the earthquake. This result clearly indicates that the change in the energy of ULF electromagnetic waves could be related to strong precursory earthquake phenomena. Moreover, changes in energy associated with strong aftershock activity were also observed 25 days after the earthquake. Finally, we present results concerning the comparison between changes in energy during night and day passes of the satellite over Haiti, which showed differences in the mean energy values, but similar results as far as the rate of the energy change is concerned.