  When an emitting spherical shell with a constant Lorentz factor turns off
emission abruptly at some radius, its high-latitude emission would obey the
relation of $\hat{\alpha}$ (the temporal index) = $2 + \hat{\beta}$ (the
spectral index). However, this relation is violated by the X-ray fares in some
gamma-ray bursts (GRBs), whose $\hat{\alpha}$ is much more steeper. We show
that the synchrotron radiation should be anisotropic when the angular
distribution of accelerated electrons has preferable orientation, and this
anisotropy would naturally lead to the steeper decay for the high-latitude
emission if the the intrinsic emission is limb-brightened. We use our simple
toy model to reproduce the temporal and the spectral evolution of the X-ray
flares. We show that our model can well interpret the steep decay of the X-ray
flares in the three GRBs selected as example. Recent simulations on particle
acceleration may support the specific anisotropic distribution of the electrons
adopted in our work. Reversely, confirmation of the anisotropy in the radiation
would give meaningful clues to the details of electron acceleration in the
emitting region.
