The critical concentrations and the critical temperatures for the microemulsion systems of {water + 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4I) + sodium di(2-ethyl-1-hexyl)sulfosuccinate (AOT) + decane) with various compositions of [bmim][BF4] have been measured. The coexistence curves for the quaternary microemulsion with the molar ratio of water to AOT being 40.8 and the mass fraction of [bmim][BF4] being 1.1.10(-4) have been determined by measuring the refractive index at constant pressure in the critical region. The critical exponent beta has been deduced from the coexistence curves. The value of beta is very close to the 3D-Ising exponent in the critical region. It was found that the addition of [bmim,][BF4] significantly reduced the lower critical temperature, which was contrary to the (water + KCl + AOT + decane} system, while the critical composition was almost kept unchanged. It may be attributed to the unique rote of the ionic liquid which is capable of modifying the physicochemical properties of microemulsions.