Reflection of the incident photons by the silicon surface is a major source of losses during photovoltaic conversion. However, these losses can be minimized by depositing an antireflection layer, usually silicon nitride SiNx: H, combined with an appropriate texturing. This layer should also provide a good passivation where a real dilemma can be arising. In contrast the surface passivation gets better with increasing Si content (large optical index for n > 2.3) and the minimum reflectivity was found for small optical index. To achieve this, one first approach consists to use a double antireflective layer with two materials of different refractive index n. Among the materials that are appropriate from the standpoint of physics and technology are SiNx:H-rich silicon, Oxynitride SiOxNy and silicon oxide SiOx. To optimize the antireflection multilayer, we have developed a numerical simulation code with Matlab software package where we have used the method of transfer matrix to solve the optical equation. These solutions permit us to plot the optical reflectivity and the absorption versus wavelengths and layer thicknesses. The optical refractive index and thicknesses of considered materials, which allowed us to have the lowest reflection, were used to simulate the electrical properties of the cell with PC1D and Silvaco software. Thus, our results showed the cell efficiency increase by 0.3% and effective reflectivity of 7.4% is obtained with a first oxide layer (n1=1.5 and d1=55nm), and a second layer of silicon nitride (n2=2.1 and d2=53nm) non-encapsulated compared to a reference solar cell (with a SARC SiN). In the case of multilayer non-encapsulated, our optimization has shown that it is possible to increase the efficiency by 0.7% with the refractive index (1.48, 2 and 2.4) and thicknesses (80, 5 and 50) nm