Magnetic Co50Pt50 films few nanometers thick have been deposited by Pulsed Laser Deposition on MgO (100) single crystal at a deposition temperature of 600 degrees C and then annealed "in situ" for different time. A very thin Pt underlayer (< 2 nm) with an incomplete coverage is used as a possible template to favour the growth of isolated grains of the magnetic layer. The correlation between the structural, microstructural and magnetic properties has been studied as a function of the annealing time. In particular, measurements gave evidence of the presence of two competing effects of the annealing treatment: formation of hard fct-CoPt phase and thermal diffusion process between Pt and CoPt layer resulting in a reduction of the crystallographic order.