  We propose an approximate second order maximum entropy ($M_2$) model for
radiative transfer in slab geometry. The model is based on the ansatz of the
specific intensity in the form of a $\Beta$-distribution. This gives us an
explicit form in its closure. The closure is very close to that of the maximum
entropy, thus an approximation of the $M_2$ model. We prove that the new model
is globally hyperbolic, sharing most of the advantages of the maximum entropy
closure. Numerical examples illustrate that it provides solutions with
satisfactory agreement with the $M_2$ model.
