The far-zone scattered field patterns of a hyperbolic reflector antenna are analyzed by using uniform geometrical theory of diffraction(UTD). The main objective of this paper is to obtain the higher order diffraction contributions which provide the continuity over the shadow boundaries of the first order solution. to obtain the scattered magnetic field characteristics, the scattered field components of the secodn-order diffraction, diffraction-reflection, diffraction-reflection-diffraction terms are added to the result of the previous research. The results of the present research are compared to those of the first order solution and the method of moments. One can observe the improvemtn of the current approach over the first order solution. also, the results of the present method agree very well with those of the moment methods especially in the transition regions near the first order diffraction shadow boundaries.