We report on an accurate experimental determination of the critical exponents of a two-dimensional magnetic phase transition in a system of amorphous ultrathin-film multilayers grown by sputtering from precise magnetization measurements. The critical exponents b, g, and d, related to the temperature dependence of the spontaneous magnetization, the initial susceptibility, and the critical magnetic polarization isotherm, respectively, have been obtained using various conventional methods of analysis from the magnetic-polarization data. These critical exponents are found to be in excellent agreement with the two-dimensional Ising model indicating that the morphological defects in the investigated system are not effective in limiting the correlation length