Peculiarities of the measurement of femtosecond lifetimes of free charge carriers in gallium arsenide grown by the method of molecular beam epitaxy are considered. The carrier lifetime is determined by a variant of the pump-probe method in which the pumping and probing radiation beams are incident onto the semiconductor sample surface at the Brewster angle. The proposed variant ensures the detection of a change in the induced refractive index even in the case of very small response signals, thus providing for a high sensitivity of measurements. It is shown that the relative signal changes near the Brewster angle reach a maximum level.