Investigating the spectral and temporal characteristics of the X-rays coming from Sagittarius A* (Sgr A*) is essential to our development of a more complete understanding of the emission mechanisms in this supermassive black hole located at the center of our Galaxy. Several X-ray flares with varying durations and spectral features have already been observed from this object. Here we present the results of two long XMM observations of the Galactic nucleus carried out in 2004, for a total exposure time of nearly 500 ks. During these observations we detected two flares from Sgr A* with peak 2-10 keV luminosities about 40 times (L_X 9 * 1034 erg/s) above the quiescent luminosity: one on 2004 March 31 and another on 2004 August 31. The first flare lasted about 2.5 ks and the second about 5 ks. The combined fit on the Epic spectra yield photon indeces of about 1.5 and 1.9 for the first and second flare respectively. This hard photon index strongly suggests the presence of an important population of non-thermal electrons during the event and supports the view that the majority of flaring events tend to be hard and not very luminous.