  We consider a relativistically moving blob consisting of an isotropic
electron distribution that Compton-scatters photons from an external isotropic
radiation field. We compute the resulting beaming pattern, i.e. the
distribution of the scattered photons, in the blob frame as well as in the
observer's frame by using the full Klein-Nishina cross section and the exact
incident photon distribution. In the Thomson regime the comparison of our
approach with Dermer 1995 results in concurrent characteristics but different
absolute number of the scattered photons by a factor of f_corr = 3.09.
Additionally, our calculation yields a slightly lower boost factor which varies
the more from the corresponding value in Dermer 1995 the higher the spectral
index p of the electron distribution gets.
