Quantitative SPECT can be well achieved if photon attenuation is taken into account in the reconstruction process. Using a transmission scan is a common approach. A dramatic simplification could be made if the attenuation map could be obtained from the emission data. In this paper, we propose a new method to estimate the attenuation map using the data consistency conditions of the attenuated Radon transform. It is based on deriving boundaries of the constant regions of the true attenuation map using an iterative algorithm. This new method is tested by Monte Carlo simulations with the attenuation and scattering effects.