One of the few methods that allows the determination of zonal thermospheric winds is the analysis of the variation of the inclination of satellite orbits. Until now mainly the diurnally averaged zonal wind velcoity was determined by this method. From the analysis of the orbit of the ballon satellite Explorer 24 (1964-76A) both the diurnal average and the diurnal variation of the zonal wind have been determined in the height region between 540-610 km. Within the limits of the accuracy of the method there results a diurnally averaged zonal wind velocity that is nearly zero. This is contrary to the results of previous investigations by a similar method where an average rotational velocity of the exosphere appreciably less than the rotational velocity of the earth has been found. The diurnal component of the zonal wind is shown to have an amplitude of 90¿65 m/sec, and the zonal wind has its maximum from West to East at 23.96¿2.33 hr local time. Both the amplitude and the phase of the diurnal component of the zonal exospheric wind velocity agree approximately with the theoretical results of Blum and Harris.