The phenomenon of the variation of azimuth due to the earth's oscillation about its instantaneous axis of rotation is of considerable importance in both astronomy and geophysics. In this paper an attempt has therefore been made to design an accurate method of determining the variation of azimuth from astronomical observations, making use of only precise horizontal circle readings on an astronomical theodolite at recorded instants of intersections of close circumpolar stars within short distances of their meridian transits on each side.The special feature of the method is that its observational procedure is exactly similar to that of time-determination by the usual method of meridian transists of stars making use of a much lesser number of stars in actual practice, and is thus much simpler and less time-consuming than any of the existing methods. Moreover the variation of azimuth obtained therefrom is free from the usual errors of clocks, declinations and right ascensions of stars, as well as adopted latitudes of stations of observations, so vital in the delicete researches on the motion of the pole.