The kU value of a commercially available miniature energy compensated Geiger-Müller (GM) detector has been determined using the modified lead attenuation method of Hough. The measurements were made in a d(48.5)-Be neutron beam produced by the superconducting cyclotron based neutron therapy facility at Harper Hospital. The unique problems associated with making measurements in a 2 ms duration pulsed beam with a 20% duty cycle are discussed. The beam monitoring system, which allows the beam pulse shape at low beam intensities to be measured, is described. By gating the GM output with a discriminator pulse derived from the beam pulse shape, the gamma-ray count rates and dead-time corrections within the 2 ms pulse and between pulses can be measured separately. The kU value of (0.0245 +/- 0.0015) determined for this GM detector is consistent with the values measured by other workers with identical and similar detectors in neutron beams with comparable, but not identical, neutron spectra.