The angular velocity spread of relativistic photoelectrons induced by a pulsed excimer laser was measured. The energy, the current density, and the pulse duration of the accelerated photoelectron were 0. 34 Mev, 0. 5 A/cm**2, and 20 ns, respectively. (The method of measurement is based on measuring Larmor radius which corresponds to the transverse component of the electron velocity). The angular velocity spread was found to be less than 8 multiplied by 10** minus **3, which means that the energy component due to the perpendicular component of beta was as small as approximately less than 17 ev.